Ch.10 - Gases

Problem 60

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Chapter 10, Problem 60

Acetylene gas, C2H21g2, can be prepared by the reaction of calcium carbide with water: CaC21s2 + 2 H2O1l2¡Ca1OH221aq2 + C2H21g2 Calculate the volume of C2H2 that is collected over water at 23 °C by reaction of 1.524 g of CaC2 if the total pressure of the gas is 100.4 kPa. (The vapor pressure of water is tabulated in Appendix B.)

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Identify the balanced chemical equation for the reaction: \( \text{CaC}_2 (s) + 2 \text{H}_2\text{O} (l) \rightarrow \text{Ca(OH)}_2 (aq) + \text{C}_2\text{H}_2 (g) \).

Calculate the moles of \( \text{CaC}_2 \) using its molar mass: \( \text{moles of CaC}_2 = \frac{\text{mass of CaC}_2}{\text{molar mass of CaC}_2} \).

Use stoichiometry to find the moles of \( \text{C}_2\text{H}_2 \) produced, knowing that 1 mole of \( \text{CaC}_2 \) produces 1 mole of \( \text{C}_2\text{H}_2 \).

Determine the partial pressure of \( \text{C}_2\text{H}_2 \) by subtracting the vapor pressure of water from the total pressure: \( P_{\text{C}_2\text{H}_2} = P_{\text{total}} - P_{\text{H}_2\text{O}} \).

Use the ideal gas law \( PV = nRT \) to calculate the volume of \( \text{C}_2\text{H}_2 \), where \( P \) is the partial pressure of \( \text{C}_2\text{H}_2 \), \( n \) is the moles of \( \text{C}_2\text{H}_2 \), \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of product formed from a given amount of reactant. In this case, understanding the stoichiometric relationship between calcium carbide (CaC2) and acetylene (C2H2) is essential to calculate the volume of gas produced from the mass of CaC2 used.

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. The Ideal Gas Law (PV=nRT) is particularly useful for calculating the volume of a gas under specific conditions. In this problem, we need to apply the gas laws to find the volume of acetylene gas produced, taking into account the total pressure and the vapor pressure of water at the given temperature.

Vapor Pressure of Water

The vapor pressure of water is the pressure exerted by water vapor in equilibrium with its liquid at a given temperature. It is crucial to consider this when collecting gases over water, as the total pressure measured includes both the pressure of the gas and the vapor pressure of water. To find the pressure of the acetylene gas alone, we must subtract the vapor pressure of water from the total pressure.

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