use information from appendix d to calculate the ph of (a) a solution that is 0.250 m in sodium formate (hcoona) and 0.100 m in formic acid (hcooh), (b) a solution that is 0.510 m in pyridine 1c5h5n2 and 0.450 m in pyridinium chloride 1c5h5nhcl2, (c) a solution that is made by combining 55 ml of 0.050 m hydrofluoric acid with 125 ml of 0.10 m sodium fluoride.

Answers

Answer 1

By using the Henderson-Hasselbalch equation, the pH of the given solutions are 4.17, 8.72, 3.83 respectively.

The Henderson-Hasselbalch equation can be used to determine how much conjugate base and acid should be mixed to create a buffer solution with a certain pH.

pH = pKa + [tex]log_{10}[/tex] ([[tex]A^-[/tex]]/[HA]), where [[tex]A^-[/tex]] stands for the molar concentration of the conjugate base (of the acid), and [HA] for the molar concentration of the weak acid, is how the Henderson-Hasselbalch equation is expressed.

As per Henderson-Hasselbalch equation,

For weak acid buffer, pH = pKa + log ([salt] / [acid])

For weak base buffer, pH = pKa + log ([salt] / [base])

(a) pKa of HCOOH = 3.77

Therefore, pH = pKa + log ([salt] / [acid])

pH = pKa + log ([HCOONa] / [HCOOH])

pH = 3.77 + log (0.250/0.100)

pH = 4.17

(b) pKa of Pyridine = 8.77

Therefore, pH = pKa + log ([salt] / [base])

pH = pKa + log ([Pyridinium chloride] / [Pyridine])

pH = 8.77 + log (0.450/0.510)

pH = 8.72

(c) pKa of HF = 3.17

Therefore, pH = pKa + log ([salt] / [acid])

pH = pKa + log ([NaF] / [HF])

pH = 3.17 + log [(0.10x 125) / (0.05 x 55)]

pH = 3.83

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Related Questions

In the titration of acetic acid and naoh, the use of the color indicator requires that excess base be added in order to detect the endpoint. Will this cause the calculated and reported mass percent of acetic acid in vinegar to be too high or too low? explain.

Answers

In the titration of acetic acid and NaOH, the excess bases added in order to detect the indicator color change endpoint will cause the calculated and reported mass percent of acetic acid in vinegar to be too high because it is assumed more base has reacted other than has actually reacted.

What is an indicator?

An indicator is a substance that changes color as the pH of the solution in which it is present changes.

Indicators are usually solutions of weak organic acids or bases. Some examples of indicators are methyl orange, methyl red, phenolphthalein, etc.

In a titration experiment, the color changes that occur in an indicator indicate the endpoint or equivalent point of the reaction.

Some indicators produce a sharp color change at the endpoint of a titration, whereas others do not.

Indicators are chosen to produce a suitable sharp color change at the endpoint of a given reaction.

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44.0 g of ice at –20.0 °c is mixed with 325 g of water at 32.1 °c. calculate the final temperature of the mixture. assume that no energy in the form of heat is transferred to the environment.

Answers

Using the specific heat capacities of water and ice, and taking into account the latent heat of melting for ice, we can calculate that the final temperature of the mixture will be 17.6 °C.

The negative value of the amount of heat lost by liquid water is equal to the amount of heat absorbed by the ice. The equation for calculating the amount of heat needed to change the temperature of a material looks like this:

Q = (t₂ - t₁) * c * m

t₂ - final temperature

t₁ - starting temperature (32.1 °C for water, -20.0 °C for ice)

c - specific heat capacity (4.186 J/g°C for water, 2.108 J/g°C for ice)

m - the mass of the material (325 for water, 44.0 for ice)

In addition, we have to take into account that some of the heat released by water is expended on melting the ice:

heat used for melting = m * l = 44.0 g * 334 J/g = 14696 J

l = latent heat of melting ice

This means that the heat released by water is expended on heating ice to 0°C, then melting that ice, then heating the ice water to the final temperature.

Heat expended by water:

Q = (32.1 °C - X) * 325 g * 4.186 J/g°C = 43670.445 J - 1360.45 J/°C * X

Heat absorbed by ice and ice water:

Q = 20.0 °C * 44.0 g * 2.108 J/g°C + 14696 J + X * 44.0 g * 4.186 J/g°C = 16551.04 J + 184.184 J/°C * X

These amounts of heat are equal:

43670.445 J - 1360.45 J/°C * X = 16551.04 J + 184.184 J/°C * X

27119.405 J = 1544.634 J/°C * X

X = 27119.405 J / 1544.634 J/°C = 17.6 °C

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Please help!!! Currently bombing chemistry!!

Answers

When pressure is constant. Temperature and volume is directly proportional.

What is explained by Gay Lussac's law?

According to Gay-Law, Lussac's the pressure of a given amount of gas, while the volume is held constant, changes directly with the absolute temperature of the gas.

Since one mole of The any ideal gas is meant to be 22.4L at STP, the gay-Lussacs law holds true. The ratios of the number of moles of gases to one another should continue to be factors and multiples of one another since this changes directly with heat (and inverse with pressure), but operates the same for all gases.

Under circumstances of constant mass and volume, Gay-law, Lussac's also known as Amonton's law, asserts that the absolute pressure and temperature of an ideal gas are directly related.

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Explain why the ideas on atoms proposed
by Dalton constitute a theory, while the ideas pro-posed by Democritus do not

Answers

The ideas on atoms proposed by Dalton constitute a theory, while the ideas proposed by Democritus do not because Democritus' theories did not explain chemical behavior and were not supported by experimental findings.

Dalton's theories were scientifically based and did explain chemical behavior; his tests revealed that the ratios in which elements were mixed were whole numbers. Democritus' theories were in line with later scientific theories, but they did not account for chemical activity. Democritus' method was not based on science, so it also lacked experimental support.

 According to the first section of Dalton's theory, all matter is composed of indivisible atoms. According to the second component of the theory, the mass and characteristics of every atom in a specific element are the same. Compounds, according to the third section, are combinations of two or more different kinds of atoms.

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Match each element to the number of electrons in its valence shell.

Match Term Definition
Carbon (C) A) Four
Hydrogen (H) B) Two
Magnesium (Mg) C) Six
Oxygen (O) D) One

Answers

Answer:

C: 4

H: 1

Mg: 2

O : 6

Explanation:

You can quickly find out the number of valence electrons by looking at where the element is on the periodic table and referring to the table that is attached.

What do we call the arrangement of elements with similar properties?

Answers

Answer:

the periodic table

Explanation:

Elements with similar properties are in columns called groups. Elements to the left of this line are metals. Elements in the same group of the periodic table have the same number of electrons in their outer shell. This gives them similar chemical properties.

Hope this helps!

Which TWO words complete the gaps? To check if the cracking of a long-chain hydrocarbon has actually produced alkenes, the gas produced can be bubbled through __________ __________.

Answers

To check in case the splitting of a long-chain hydrocarbon has created alkenes, the gas created can be bubbled through natural gas or aromatic rich petroleum gas.

The first beginning of cracking of hydrocarbons is alkanes. The items of splitting incorporate alkanes and alkenes, individuals of a different homologous series.

An alkene could be a hydrocarbon that contains a carbon-carbon twofold bond. The longer alkanes are warmed, and their vapors are passed over a hot catalyst. This causes covalent bonds to break and change.

In thermal breaking, tall temperatures (ordinarily within the run of 450°C to 750°C) and weights (up to approximately 70 climates) are utilized to break the huge hydrocarbons into littler ones.

Thermal splitting gives blends of items containing tall extents of hydrocarbons with two-fold bonds - alkenes.

Catalytic cracking uses a temperature of approximately 550°C and a catalyst known as a zeolite which contains aluminum oxide and silicon oxide. Steam cracking uses a higher temperature of over 800°C and no catalyst.

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Question 1 (1 point) Some historians think that drinking wine from (answer) -glazed vases contributed to the fall of the Roman Empire. ​

Answers

Some historians think that drinking wine from lead-glazed vases contributed to the fall of the Roman Empire.

What is wine and ancient Rome?

Rome played a significant role in the history of wine. The first people to have an impact on winemaking on the Italian peninsula were the ancient Greeks and Etruscans.

Scientific advancements and an expanding understanding of winemaking were both brought about by the expansion of the Roman Empire. Rome had a significant impact on the history of today's important wine-producing regions in France, Germany, Italy, Portugal, and Spain.

Because the Romans believed that wine was a daily necessity, the beverage was "democratic" and widely available to everyone, including slaves, peasants, and aristocrats, both men and women. To ensure a consistent supply of wine for Roman soldiers and colonists, viticulture and wine production spread throughout the empire.

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the process of phosphorylation: group of answer choices may energize the target molecule adds a phosphate group to a molecule all are correct may change the shape of the target molecule releases a phosphate group from one molecule

Answers

The correct answer is All of the answer choices are correct.

A biochemical process that involves the addition of phosphate to an organic compound. In biological systems, this reaction is vital for the cellular storage and transfer of free energy using energy carrier molecules.

The first step in the metabolism of carbohydrates is frequently their phosphorylation. Because the phosphate group stops the molecules from migrating back across the transporter, phosphorylation enables cells to store carbohydrates. Glucose phosphorylation is a crucial step in the metabolism of sugar.

The chemical formula for the first step of glycolysis, which involves the conversion of D-glucose to D-glucose-6-phosphate, is provided by

          D-glucose + ATP → D-glucose-6-phosphate + ADP

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The complete question is :

The process of phosphorylation

(a) adds a phosphate group to a molecule.

(b) may energize the target molecule.

(c) removes a phosphate group from a molecule.

(d) may change the shape of the target molecule.

(e) All of the answer choices are correct

How is this substance classified?

Arrhenius Base

Bronsted-Lowry Acid

Arrhenius Acid

Bronsted-Lowry Base

Answers

According to the Bronsted-Lowry concept, acids are proton donors and bases are proton acceptors. In this reaction, NH3 gains protons and H2O loses protons. NH3 is therefore a Bronsted-Lowry base.

NH3   +   H2O    ⇒   NH4+                            + OH-

Base       Acid       Conjugate acid       Conjugate base

A basic solution is formed when ammonia dissolves in water. A small amount of dissolved ammonia reacts with water to form ammonium hydroxide which dissociates into ammonium and hydroxide ions. All these processes are reversible. Hydrogen bonds are weak bonds that are easily broken to form H+ and OH ions. This reaction also has multiple reactants, but only one product.

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In an experiment trying to dissolve sugar in water, a person boils water in a pot on the stove and then puts the water and the sugar in a cup. That person times how long it takes to dissolve the sugar.

Which of the following factors is this person testing?

Answers

The factors for dissolving sugar.

Warmth or Fahrenheit minus 0.2 ranges Celsius dissolves the sugar in water. because of sugar's soluble nature, it's miles present at any temperature or stress in liquid water. about 10 mins for this.

Time will depend upon many stuff.Quantity of Sugar: extra sugar - extra timeAmount of water: extra water- much less timeThe temperature of water: better the temperature- much less timeWhether the contents are being stirred. With stirring- much less timeThe crystal size of sugar. excellent sugars - less time. Coarse sugar- greater time.

Sugar dissolves quicker in hot water than it does in bloodless water due to the fact warm water has extra strength than bloodless water. whilst water is heated, the molecules benefit energy and, therefore, pass quicker. As they flow faster, they come into contact with the sugar more often, inflicting them to dissolve more quickly.

The dissolution of sugar in water is a bodily change because it no longer brings about the formation of a new substance. it's miles a reversible alternative as sugar and water may be extracted and returned from the solution through the method of crystallization observed by evaporation.

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How are all of Earth's water reservoirs connected to the ocean?

Answers

Answer:

Through intermolecular constant tube routes

The reaction you will be performing requires a source of chloride ion, which is the required nucleophile. A sodium chloride solution would be much more safe than a hydrochloric acid solution. Why is acid required?.

Answers

Acid protonates the hydroxyls of the starting material, turning them into a better leaving group.

A salt is a compound formed when the negative ions from an acid combine with the positive ions of a base.

Neutralization is a chemical reaction between an acid and a base that takes place in a water solution, the products of which are water and salts.

NaOH (aq) + HCl (aq) → NaCl (aq) + H₂O (l)

What is crystallization?The process of turning a liquid substance into a highly structured solid whose atoms or molecules are arranged in a well defined three-dimensional crystal lattice is known as crystallisation. A unit cell is a crystal's tiniest discrete component. There are millions of these unit cells throughout the crystal. The primary use of crystallisation is as a separation process to separate pure crystals of a chemical from an impure mixture. The process of crystallisation is used to extract pure salt from seawater, which is another significant use. To create pure alum crystals from impure alum, crystallisation can also be used. Since it also gets rid of the soluble contaminants, crystallisation is believed to be more efficient in such circumstances than evaporation.

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The amount of water vapor in the atmosphere is measured as blank______, whereas blank______ is the ratio of the amount of water vapor to the maximum amount of water vapor that can be held by an air mass.

Answers

The amount of water vapor in the atmosphere is measured as blank humidity whereas blank relative humidity is the ratio of the amount of water vapor to the maximum amount of water vapor that can be held by an air mass.

Solar energy is absorbed and stored as latent heat, which is then transported to higher latitudes and released as the water cools and changes phase. any gas that absorbs infrared radiation (net heat energy) emitted from the Earth's surface and reradiates it back to the Earth's surface, thereby contributing to the greenhouse effect The most significant greenhouse gases are carbon dioxide, methane, and water vapour. Water vapor is the most abundant greenhouse gas on Earth. It is responsible for roughly half of the greenhouse effect, which occurs when gases in the Earth's atmosphere trap the Sun's heat. Greenhouse gases enable us to live on our planet.

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is nh4hco3 acidic, neutral, or basic? if is it not neutral, compare their ka and kb values to determine if it is acidic or basic and explain your reasoning

Answers

Ammonium acetate is a salt formed from ammonium hydroxide (weak base) and acetic acid (weak acid).

NH4OH + CH3COOH 1  CH3COO-NH4+ + H2O

Here, pKb for NH4OH = 4.8

And, pKa for CH3COOH = 4.74

Now, for a salt of weak acid and weak base

pH = 7 + 0.5 (pKa - pKb)

pH = 7 + 0.5 (4.74 - 4.8)

pH = 7 + 0.5 (- 0.06)

pH = 7 - 0.03

pH = 6.97

Since, pH is slightly less than 7, it is slightly acidic (almost neutral).

Ammonium acetate and acetic acid are frequently combined to form a buffer solution because they are the salt of two weak acid and base. At low pressures, ammonium acetate is flammable. As a result, while preparing samples for mass spectrometry, it has been utilised to substitute cell buffers that include non-volatile salts. Due to this, it is frequently used as a buffer for mobile phases in HPLC systems with ELSD detection. This has also been done with other volatile salts, like ammonium formate.

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The Mass of an empty bottle
is 4 kg if the mass When
filled with Cold water
12.5 kg Find
A. Mass of empty bottle.

Answers

Water has a 1 g/cm3 density. Weight of water in grammes when a bottle is completely filled with that amount of water.

Density bottle volume:

The empty density bottle weighs M1 = 4 kg.

Bottle weight plus water equals 12.5 kg Bottle weight plus water equals 12.5 kg Mass of water filling the density container to the top equals M2 — M1 (12.5—4=8.5 kg).

However, 1 g of water has a volume of 1 cc.

water volume equals 8.5 cubic centimetres, or 8.5 ml, in a density bottle.

Define density.

The ratio between a substance's mass and volume is referred to as its density.

Volume/Mass = Density

The substance's mass per unit of volume is known as its density (volumetric mass density or specific mass). Although the Latin letter D may also be used, the sign most frequently used for density is (the lower case Greek letter rho). Mass divided by volume is the definition of density in mathematics: where is the density, m is the mass, and V is the volume.

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9. If a solution has a pOH of 5.7 what is its pH?

Answers

PH scale is from 1 till 14 some being alkaline and the others acidic … 5.7 in a weak acidic pH since it is close to pH7 which is a neutral pH

could you crystallize one enantiomer of mandelic acid from a racemic mixture (using the typical achiral solvents found in our lab) without preparing a diastereomeric salt? why or why not?

Answers

No. We cannot crystalline one enantiometer of mandolin acid from a racemic mixture without preparing a disatereomeric salt because enantiomers have the same solubility in achiral solvents, one enantiomer can not be selectively crystallized from the solution.

What is crystallization?

A supersaturated solution nucleates the solute in the process of crystallization, which is a technique for turning a solution into a solid under the control of chemical equilibrium. The result is the formation of uniform particles with well defined morphologies that easily dissolve again. Crystals are frequently fragile.

Precipitation from a solution, freezing, and, less frequently, direct deposition from a gas are a few processes that can result in the formation of crystals.

Hence, it cannot be crystallized.

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Do stable isotopes tend to have a similar amount of protons to neutrons or a very different amount of protons to neutrons? Why do you think that is? State your answer in 2-4 sentences.

Answers

Stable isotopes tend to have a very different amount of protons to neutrons because the ratio of protons and neutrons is nearly 1 or less than 1.5, whereas the number of protons and neutrons in unstable isotopes is greater than 1.5

What are isotopes of elements?

Isotopes of elements are atoms of the same elements having the same number of protons but different numbers of protons.

Isotopes of elements may either be stable isotopes or unstable isotopes.

Stable isotopes are isotopes whose nuclei do not spontaneously decay and emit nuclear particles as well as radiation. Stable isotopes usually have a proton and neutron ratio that is less than 1 : 1.5.

Unstable isotopes are isotopes whose nuclei spontaneously decay and emit nuclear particles as well as radiation. Unstable isotopes usually have a proton and neutron ratio that is greater than 1 : 1.5.  The spontaneous decay of unstable isotopes is due to the presence of the excess neutrons in the nucleus of the atom.

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10. Personal eyeglasses provide as much protection as
a. A face shield
b. Safety glasses
c. Splash Proof chemical goggles
d. None of the above

Answers

Answer: D- None of the above

-

Eliminate a face shield, a face shield covers your entire face, while glasses only cover your eyes and around your eyes. Glasses are glass while shield covers are usually plastic.

Eliminate Safety glasses because, again, eye glasses only cover your eyes and the surrounding areas of your eyes with glass, the gaps beside and under them allow chemical incidents to go into your eyes. Safety glasses wrap around your head and usually completely sheild you eyes.

Eliminate splash proof chemical goggles, this would fall into the category of safety glasses.

Which option best describes this type of reaction?

Answers

Answer: combustion and exothermic

Explanation: I took the test

Combustion and exothermic describes this type of reaction.

Why are exothermic combustion processes the norm?

Products are the most stable and exothermic for every combustion because they are (of an exothermic process) more stable than reactants (whose energy is substantially lower).

A material burns when it reacts with oxygen during combustion, producing energy in the form of heat and light. The temperature rises when the energy generated by an exothermic reaction is released as heat.

Burning and combustion are both terms for the exothermic reaction in which heat is released. Redox chemical processes, which are primarily what occur during combustion, require an oxidant, often air oxygen. In any event, a high-temperature exothermic combustion process occurs when anything burns.

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A group of students working in a chemistry lab are planning a procedure to neutralize hydrochloric acid (HCl, strong acid). How should they BEST accomplish this?

Titrate a strong acid into the strong acid.
Titrate a strong base into the strong acid.
Titrate a weak base into the strong acid.
Titrate a weak acid into the strong acid.

Answers

To neutralize hydrochloric acid (HCl, strong acid), students should Titrate a strong base into the strong acid.

HCL or hydrochloride acid is strong acid found in the digestive system of animals and humans , this acid in gut helps in break down of protein and absorb essential nutrients, and it helps to control viruses and bacteria that might infect the stomach. It is formed when hydrochloride gas mixes with the water.

A strong acid like HCL can be neutralize with a help of strong base like sodium hydroxide (NaOH). The reaction between sodium hydroxide (NaOH) and hydrochloric acid (HCl) is a neutralization reaction which results in the formation of a salt, sodium chloride (NaCl), and water (H2O).

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PLEASE HELP, AWARDING BRAINLIEST!

Answers

The shortest wavelength emitted from the initial configuration of 6 d1 is 327 nm. Here the first energy level is 6 and the last level is infinity.

What is wavelength?

Wavelength is of a radiation is the distance travelled by a wave. As the wavelength of a wave gets smaller its energy increases.

The relation between wavelength and energy levels is given below:

[tex]\frac{1}{\lambda } = R [\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}][/tex]

here, R is a constant equal to 1.1 × 10⁷ and n₁ and n₂ are two energy level.

The smallest wavelength of light emitted from hydrogen with n₁ =6 and n₂ = ∞ can be calculated as follows:

[tex]\frac{1}{\lambda } = 1.1\times 10^{7} [\frac{1}{6^{2}}-\frac{1}{\infty ^{2}}] =30.5\times 10^{5} cm[/tex]

[tex]\lambda = \frac{1}{30.5\times 10^{5}}= 327 \textup{ nm}[/tex]

Hence, wavelength of the light emitted is 327 nm.

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what volume of concentrated aqueous ammonia must be diluted to 1.00 l to make a solution that has a molarity of 1.85 m. concentrated nh3 (aq) is 15 m. report the volume of concentrated aqueous ammonia in milliliters.

Answers

The volume of concentrated aqueous ammonia must be diluted to 1.00 l to make a solution that has a molarity of 1.85 m. concentrated nh3 (aq) is 15 m. report the volume of concentrated aqueous ammonia in milliliters is 123 mL

The number of moles of solute must always remain constant while diluting solutions, which is the most crucial thing to remember.

In other words, the amount of solute in the concentrated sample must be identical to the amount of solute in the diluted solution.

The concentration is the number of moles per unit volume. So

c=n/V

n=CV

n= 1.85x1

n=1.85

Now your task is to determine what volume of the concentrated solution would contain this many moles of ammonia.

Plugging the values, we get

V=1.85/15

V=0.123 L

Now for dilution calculations, we have

C1V1=C2V2

V1=C2/C1.V2

V1=1.85/15x1.00= 123 mL

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How does the temperature of water change if you heat it after it has already
reached the boiling point?

Answers

Answer:

It will not change, even if you still heat it.

Explanation:

what enthalpy change would be associated with the production of 45.0 l oxygen at 0.80 atm and 300 k?

Answers

To Find  enthalpy change

Let's count the moles of gaseous oxygen first. Using n= m/M

=n(O)= 32.00/2×15.99)mol

= n(O)= (32.00/31.98) mol

=n(O)= 1.00mol

Let's now change every relevant value in the equation PV=nRT.

=P× 20.0L= 1.00mol× 0.0821[tex]L atm mol^{-1} K^{-1}[/tex]× 303.15K

= P× 20.0= 1.00× 0.0821atm× 303.15

[tex]P=(0.0821*300/20) atm[/tex]

P= 1.24atm

Therefore, 1.24 atm is the pressure that the oxygen gas is exerting.

The ideal gas equation is what.

The macroscopic characteristics of ideal gases are related by the ideal gas law (PV = nRT). A gas is said to be ideal if its particles don't interact with one another and don't occupy any space.

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I need help
Consider the combustion of methane:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)

Which reactant is decreasing at the fastest rate?

Answers

Consider the combustion of methane:

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

The reactant is decreasing at the fastest rate is CH₄.

Combustion of methane CH₄ is a reaction between methane and oxygen present in the air to produce carbon dioxide and water.

the reaction involved is

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

The limiting reagent in this reaction is methane because the other reactant is oxygen which is present in air is always there ion excess. thus, the amount of carbon dioxide and water produced in the combustion of methane will depend upon the amount of methane burnt .

Thus,  Consider the combustion of methane:

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(g)

The reactant is decreasing at the fastest rate is CH₄.

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Which atom in the ground state has five electrons
in its outer level and ten electrons
in its kernel?
A) C
B) Si
C) CI
D) P

Answers

Phosphorus atom in the ground state has five electrons in its outer level and ten electrons in its kernel.

What is atom?

The smallest component of ordinary stuff that makes up a chemical element is an atom. Atoms that are neutral or ionized make up every solid, liquid, gas, and form of plasma. Atoms are incredibly tiny, measuring typically 100 picometers across. Ion charge or zero (neutral) electric charge.

Space makes up the majority of an atom. The rest is made up of a cloud of negatively charged electrons surrounding a positively charged nucleus made up of protons and neutrons. Compared to electrons, which are the lightest charged particles in nature, the nucleus is small and dense.

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wich statement indicates that a chemical reaction has taken place

Answers

The correct answer of chemical reaction is option (C) an odor is produced by burning a sugar.

An odor is produced by burning a sugar is a statement which indicates that a chemical reaction has taken place.

A chemical reaction is a manner that leads to the chemical transformation of 1 set of chemical substances to some other. A chemical reaction is a technique in which one or extra materials, also called reactants, are converted to 1 or greater special materials, known as merchandise. substances are both chemical factors or compounds.

A chemical reaction is a system in which reactants react chemically and convert into merchandise by chemical transformation. as an example, breathing we inhale oxygen which reacts with glucose and produces carbon dioxide, water and energy.

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a chemical system that results from a chemical reaction has two important components among others in a blend. the joint distribution describing the proportions x and y of these two components is give by f(x,y)

Answers

The marginal density function of X and Y is 1 and thus they are probability density functions and the probability of the conditions in (c) and (d) is 0.2 and 0.8 respectively.

A probability is a number that expresses the likelihood or chance that a given event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

A probability density function, also known as the density of a continuous random variable in probability theory, is a function whose value at each given sample in the sample space may be read as offering a relative likelihood that the random variable's value will be near to that sample. Probability density functions are statistical measures that are used to predict the outcome of a discrete value. The probability density function is nonnegative all the way through, and the area under the entire curve is equal to one.

a) The marginal density of X is

[tex]f_X (x) = \int\limits^x_0 {f_{X,Y} (x,y)} \, dx = \int\limits^x_0 {2} \, dx = 2x[/tex]

If it is a pdf, then

[tex]\int\limits^1_0 {f_X(x)} \, dx = 1[/tex]

[tex]\int\limits^1_0 {2x} \, dx = x^2 |_0^1 = 1[/tex]

Since integral is 1, marginal density function of X is pdf.

b) The marginal density of Y is

[tex]f_Y (y) = \int\limits^y0 {f_{X,Y} (x,y)} \, dy = \int\limits^y_0 {2} \, dy = 2y[/tex]

If it is a pdf, then

[tex]\int\limits^1_0 {f_Y(y)} \, dy = 1[/tex]

[tex]\int\limits^1_0 {2y} \, dy = y^2 |_0^1 = 1[/tex]

Since integral is 1, marginal density function of Y is pdf.

c)

       [tex]P (x < 0.2,y > 0.5) = \int\limits^1_{0.5}\int\limits^{0.2}_0 {f_{X,Y} (x,y) \, dx \, dy = \int\limits^1_{0.5}\int\limits^{0.2}_0 2dxdy[/tex]

       [tex]= \int\limits^1_{0.5} [2x]_0^{0.2}dy = 0.4[y]_{0.5}^1 = 0.4 (1 - 0.5) = 0.2[/tex]

d)

      [tex]P (x < 0.8,y > 0.5) = \int\limits^1_{0.5}\int\limits^{0.8}_0 {f_{X,Y} (x,y) \, dx \, dy = \int\limits^1_{0.5}\int\limits^{0.8}_0 2dxdy[/tex]

      [tex]= \int\limits^1_{0.5} [2x]_0^{0.8}dy = 1.6[y]_{0.5}^1 = 1.6 (1 - 0.5) = 0.8[/tex]

The complete question is:

A chemical system that results from a chemical reaction has two important components in a blend among others. The joint distribution that describes the proportion X and Y of these two components is given by f(x,y) = 2 for 0 < x < y < 1 and f(x,y) = 0 otherwise. (a) Find the marginal density function of X and verify if it is a pdf. (b) Find the marginal density function of Y and verify if it is a pdf. (c) Find the probability that the component proportions produce results X < 0.2, Y > 0.5. (d) Find the probability that the component proportions produce results X < 0.8, Y > 0.5.

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