Ch.10 - Gases: Their Properties & Behavior

Problem 138

Chapter 10, Problem 138

When solid mercury(I) carbonate, Hg2CO3, is added to nitric acid, HNO3, a reaction occurs to give mercury(II) nitrate, Hg1NO322, water, and two gases A and B: Hg2CO31s2 + HNO31aq2¡ Hg1NO3221aq2 + H2O1l 2 + A1g2 + B1g2 (a) When the gases are placed in a 500.0-mL bulb at 20 °C, the pressure is 258 mm Hg. How many moles of gas are present?

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Identify the gases A and B produced in the reaction. In this reaction, the gases are likely carbon dioxide (CO2) and nitrogen dioxide (NO2).

Use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

Convert the given pressure from mm Hg to atmospheres (atm) as the gas constant R is typically used with pressure in atm. Use the conversion factor 1 atm = 760 mm Hg.

Convert the temperature from degrees Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Substitute the converted pressure, the volume in liters, the converted temperature, and the gas constant (use R = 0.0821 L atm / K mol for consistency) into the ideal gas law equation to solve for n, the number of moles of gas.

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. Here, P is the pressure in atmospheres, V is the volume in liters, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. This law is essential for calculating the number of moles of gas produced in a reaction when given the pressure, volume, and temperature.

Gas Pressure Units

Gas pressure can be measured in various units, including mm Hg, atm, and pascals. In this question, the pressure is given in mm Hg, which can be converted to atmospheres (1 atm = 760 mm Hg) for use in the Ideal Gas Law. Understanding how to convert between these units is crucial for accurate calculations in gas-related problems.

Stoichiometry of Gas Reactions

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In this case, knowing the balanced chemical equation allows us to determine the moles of gases produced from the reaction of mercury(I) carbonate with nitric acid. This understanding is vital for calculating the number of moles of gases A and B formed during the reaction.

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Related Practice

Textbook Question

Assume that you take a flask, evacuate it to remove all the air, and find its mass to be 478.1 g. You then fill the flask with argon to a pressure of 2.15 atm and reweigh it. What would the balance read in grams if the flask has a volume of 7.35 L and the temperature is 20.0 °C?

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Textbook Question

The apparatus shown consists of three temperature-jacketed 1.000-L bulbs connected by stopcocks. Bulb A contains a mixture of H₂O(g), CO₂(g), and N₂(g) at 25 °C and a total pressure of 564 mm Hg. Bulb B is empty and is held at a temperature of -70 °C. Bulb C is also empty and is held at a temperature of -190 °C. The stopcocks are closed, and the volume of the lines connecting the bulbs is zero. CO₂ sublimes at -78 °C, and N₂ boils at -196 °C.

(a) The stopcock between A and B is opened, and the system is allowed to come to equilibrium. The pressure in A and B is now 219 mm Hg. What do bulbs A and B contain?

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Textbook Question

(b) How many moles of H₂O are in the system?

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Open Question

Consider the combustion reaction of 0.148 g of a hydrocarbon with the formula CnH2n+2 in an excess of O2 within a 400.0-mL steel container. Before the reaction, the gaseous mixture had a temperature of 25.0 °C and a pressure of 2.000 atm. After complete combustion and heat loss, the products and excess O2 had a temperature of 125.0 °C and a pressure of 2.983 atm. (a) What is the formula and molar mass of the hydrocarbon? (b) What are the partial pressures in atmospheres of the reactants? (c) What are the partial pressures in atmospheres of the products and the excess O2?

Textbook Question

A mixture of CS21g2 and excess O21g2 is placed in a 10.0-L reaction vessel at 100.0 °C and a pressure of 3.00 atm. A spark causes the CS2 to ignite, burning it completely, according to the equation CS21g2 + 3 O21g2¡CO21g2 + 2 SO21g2 After reaction, the temperature returns to 100.0 °C, and the mixture of product gases (CO2, SO2, and unreacted O2) is found to have a pressure of 2.40 atm. What is the partial pressure of each gas in the product mixture?

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