A piece of dry ice (solid carbon dioxide) with a mass of 28.8 g sublimes (converts from solid to gas) into a large balloon. Assuming that all of the carbon dioxide ends up in the balloon, what is the volume of the balloon at 22 °C and a pressure of 742 mmHg?

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Convert the mass of dry ice (28.8 g) to moles using the molar mass of carbon dioxide (CO_2), which is approximately 44.01 g/mol.

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

Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature (22 °C).

Convert the pressure from mmHg to atm, knowing that 1 atm = 760 mmHg.

Substitute the values for n (moles of CO_2), R (0.0821 L·atm/mol·K), T (temperature in Kelvin), and P (pressure in atm) into the ideal gas law equation to solve for the volume V.

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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 is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the volume of a gas when the other variables are known.

Molar Mass of Carbon Dioxide

The molar mass of carbon dioxide (CO2) is essential for converting the mass of dry ice into moles. Carbon dioxide has a molar mass of approximately 44.01 g/mol, which is calculated by adding the atomic masses of one carbon atom (12.01 g/mol) and two oxygen atoms (16.00 g/mol each). Knowing the molar mass allows us to determine how many moles of CO2 are present in the 28.8 g of dry ice.

Gas Behavior Under Different Conditions

Gases behave differently under varying conditions of temperature and pressure. According to the principles of gas behavior, an increase in temperature typically leads to an increase in volume if pressure is held constant, and vice versa. Understanding these relationships is crucial for predicting how the volume of gas will change under specific conditions, such as the 22 °C and 742 mmHg mentioned in the question.

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A weather balloon is inflated to a volume of 28.5 L at a pressure of 748 mmHg and a temperature of 28.0 °C. The balloon rises in the atmosphere to an altitude of approximately 25,000 ft, where the pressure is 385 mmHg and the temperature is -15.0 °C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

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Textbook Question

A 1.0-L container of liquid nitrogen is kept in a closet measuring 1.0 m by 1.0 m by 2.0 m. Assuming that the container is completely full, that the temperature is 25.0 °C, and that the atmospheric pressure is 1.0 atm, calculate the percent (by volume) of air that is displaced if all of the liquid nitrogen evaporates. (Liquid nitrogen has a density of 0.807 g/mL.)