(a) A sample of hydrogen gas is generated in a closed...

(a) A sample of hydrogen gas is generated in a closed container by reacting $1.750 \mathrm{~g}$ of zinc metal with $50.0 \mathrm{~mL}$ of $1.00 \mathrm{M}$ hydrochloric acid. Write the balanced equation for the reaction, and calculate the number of moles of hydrogen formed, assuming that the reaction is complete. (b) The volume over the solution in the container is 150 mL. Calculate the partial pressure of the hydrogen gas in this volume at $25^{\circ} \mathrm{C}$, ignoring any solubility of the gas in the solution. (c) The Henry's law constant for hydrogen in water at $25^{\circ} \mathrm{C}$ is $7.7 \times 10^{-6} \mathrm{~mol} / \mathrm{m}^{3}-\mathrm{Pa}$. Estimate the number of moles of hydrogen gas that remain dissolved in the solution. What fraction of the gas molecules in the system is dissolved in the solution? Was it reasonable to ignore any dissolved hydrogen in part (b)?

(a) A sample of hydrogen gas is generated in a closed container by reacting $1.750 \mathrm{~g}$ of zinc metal with $50.0 \mathrm{~mL}$ of $1.00 \mathrm{M}$ hydrochloric acid. Write the balanced equation for the reaction, and calculate the number of moles of hydrogen formed, assuming that the reaction is complete.
(b) The volume over the solution in the container is 150 mL. Calculate the partial pressure of the hydrogen gas in this volume at $25^{\circ} \mathrm{C}$, ignoring any solubility of the gas in the solution. (c) The Henry's law constant for hydrogen in water at $25^{\circ} \mathrm{C}$ is $7.7 \times 10^{-6} \mathrm{~mol} / \mathrm{m}^{3}-\mathrm{Pa}$. Estimate the
number of moles of hydrogen gas that remain dissolved in the solution. What fraction of the gas molecules in the system is dissolved in the solution? Was it reasonable to ignore any dissolved hydrogen in part (b)?

Key Concepts

Balanced Chemical Equation

A balanced chemical equation clearly shows the reactants and products in a reaction along with their stoichiometric coefficients, ensuring the law of conservation of mass is satisfied. It serves as the foundation for any quantitative analysis in a chemical reaction since it describes how much of each substance reacts and is produced.

Limiting Reagent

The concept of the limiting reagent involves identifying which reactant is completely consumed first in a chemical reaction, thereby limiting the amount of products that can be formed. This concept is crucial for accurately determining the yield of a reaction and is applied by comparing the mole ratios of the reactants to those required by the balanced equation.

Stoichiometry

Stoichiometry is the quantitative relationship between the amounts of reactants and products in a chemical reaction. It uses the coefficients from a balanced chemical equation to calculate the moles of products formed or reactants needed, facilitating conversions between mass, moles, and volume when necessary.

Ideal Gas Law

The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT, where R is the universal gas constant. This concept is widely used to predict or calculate one of these properties when the other three are known, under conditions that approximate ideal behavior.

Partial Pressure

Partial pressure refers to the pressure that each individual gas in a mixture would exert if it occupied the whole volume by itself at the same temperature. In gas mixtures or when calculating gas collection over a liquid, partial pressures are essential for understanding and quantifying the contribution of each gas component.

Henry's Law

Henry's law describes the relationship between the concentration of a gas dissolved in a liquid and the partial pressure of that gas above the liquid. It is expressed with a proportionality constant (Henry's constant) and is used to estimate how much of a gas will dissolve in a liquid under given conditions, which is important in processes that involve gas-liquid equilibrium.

Transcript

00:01 Okay, a sample of hydrogen gas is generated in a closed container.

00:25 The reaction has 1 .750 grams of zinc reacting with 50 .0 milliliters of 1 .00 molar of hydrochloric acid.

00:45 We're going to write the balanced chemical equation and calculate the number of moles of hydrogen formed.

00:53 Balanced equation, moles of h2 formed.

01:09 First, our balanced chemical equation, zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas.

01:28 We'll balance the equation as follows.

01:32 Now we're going to do a simple limiting reactant problem, and first we're going to calculate moles of both of our reactants.

01:42 Let's switch colors.

01:46 Calculate moles of zinc, we're going to take our mass of zinc, multiply by the molar mass of zinc, which i wrote down a moment ago, 65 .390.

02:06 0 .02676 moles of zinc.

02:14 Second, let's calculate our moles of hydrochloric acid.

02:25 That will equal our volume in this volume in liters, multiplied by the molarity.

02:54 Next, we're going to do our limiting reactant, and i'm going to cheat a little bit, and do a mole box.

03:04 We have my coefficients, how many moles i have, how many moles i need, and how many moles of excess.

03:19 I think we have hcl, my coefficients are 1 and 2.

03:31 Moles that we have, we're calculated as, let me raise some of this, and 0 .0500.

03:49 To find the number that goes right here, i take this times 1 divided by 2, and this gives me 0 .00126.

04:09 26, i believe.

04:16 Is that a 7 ?176.

04:48 And i find the number that goes right here.

04:52 Take this number times divide.

04:55 This is 0 .05320.

05:02 So this is my limiting.

05:05 The hcl is my limiting reactor.

05:07 So i'm going to use my hydrochloric acid moles and my mole ratio of 2 to 1 to come up with 0 .02 .2.

05:39 5 .0 moles of h2.

05:45 This is how many moles of h2 are produced.

05:54 Part b says the volume over the solution in the container is 150 milliliters...

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