Question

Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc. $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose \(240 . \mathrm{mL}\) of hydrogen gas is collected at \(30 .{ }^{\circ} \mathrm{C}\) and has a total pressure of \(1.032\) atm by this process. What is the partial pressure of hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor pressure of water is 32 torr at \(30^{\circ} \mathrm{C}\).)

Short answer

The partial pressure of hydrogen gas in the sample is 0.990 atm, and 0.644 g of zinc must have reacted to produce this quantity of hydrogen gas.

Step-by-step solution

Calculate the partial pressure of water vapor

First, we need to convert the vapor pressure of water, given in torr, to atm. We know that 1 atm = 760 torr. So: P_water (atm) = \( \frac{32 \, \text{torr}}{760 \, \text{torr/atm}} \)= 0.042 atm

Calculate the partial pressure of hydrogen gas

Now, we will use Dalton's Law of Partial Pressures to find the partial pressure of hydrogen gas: P_total = P_H2 + P_water P_H2 = P_total - P_water P_H2 = 1.032 atm - 0.042 atm = 0.990 atm

Find the moles of hydrogen gas

Next, we will use the Ideal Gas Law to find the moles of hydrogen gas. The Ideal Gas Law is given by: PV = nRT In this case, we know the volume (V) is 240 mL, which needs to be converted to L: V = 240 mL × \( \frac{1\, \text{L}}{1000\, \text{mL}} \) = 0.240 L We also know the temperature (30°C) must be converted to Kelvin (K) to use in the Ideal Gas Law: T = 30°C + 273.15 = 303.15 K We can now find the moles of hydrogen gas (n) using the ideal gas law formula: n = \( \frac{PV}{RT} \) n_H2 = \( \frac{(0.990\, \text{atm})(0.240\, \text{L})}{(0.08206\, \text{L atm/mol K})(303.15\, \text{K})} \) = 0.00986 mol

Calculate the mass of zinc

Finally, we will use stoichiometry to find the amount of zinc required for the reaction. From the balanced chemical equation, we have: Zn (s) + 2 HCl (aq) → ZnCl2 (aq) + H2 (g) 1 mole of Zn reacts to produce 1 mole of H2. Therefore, the moles of Zn required are equal to the moles of H2 produced: n_Zn = n_H2 = 0.00986 mol Now, we can calculate the mass of zinc required using its molar mass (65.38 g/mol): mass_Zn = n_Zn × molar mass of Zn mass_Zn = 0.00986 mol × 65.38 g/mol = 0.644 g So, the partial pressure of hydrogen gas is 0.990 atm, and the amount of zinc required to produce this quantity of hydrogen gas is 0.644 g.

Key concepts

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures is a simple yet important concept in chemistry. It states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases. The partial pressure is the pressure that a gas would exert if it occupied the entire volume on its own.
You can think of it as each gas contributing its share to the total pressure, based on its mole fraction. For example, in our exercise, the total pressure is the sum of the pressure from hydrogen gas and water vapor. By subtracting the known vapor pressure of water from the total pressure, we can calculate the partial pressure of hydrogen gas.
Remember, partial pressures are crucial when dealing with gas mixtures, especially in reactions involving gases collected over water. Understanding them allows you to accurately determine the pressures and moles of gases involved in such reactions.

Reaction Stoichiometry

Reaction stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It allows us to determine the amount of each substance involved in a reaction based on the balanced chemical equation. This concept is all about ratios—how one material reacts with another in fixed proportions.
In the exercise, we use the stoichiometric relationship derived from the balanced equation of zinc reacting with hydrochloric acid. The equation tells us that one mole of zinc produces one mole of hydrogen gas.

• This 1:1 molar ratio is key to finding out how much zinc is required to produce a specific amount of hydrogen gas.
• In this case, since we determined the moles of hydrogen, we know this is also the moles of zinc reacted, as per the reaction stoichiometry.

Understanding stoichiometry is fundamental when preparing chemical reactions, ensuring that all reactants are used efficiently without excess waste.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature. It's an essential concept in understanding the behavior of gases collected over liquids, as vapor pressure affects the total pressure of the gas collected.
In the exercise, the hydrogen gas collects over water and thus becomes saturated with water vapor. The vapor pressure of water at a given temperature must be considered to find the actual pressure of the gas of interest.

• At 30°C, the vapor pressure of water is 32 torr, which is approximately 0.042 atm.
• This pressure directly contributes to the total pressure, and must be subtracted to find the partial pressure of the dry hydrogen gas.

Knowing how to account for vapor pressure is crucial when working with gases over liquids, ensuring the accuracy of pressure measurements and subsequent calculations.