Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.5 - Gases

Problem 52

Chapter 5, Problem 52

A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 °C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 °C?

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Identify the initial and final conditions of the gas: initial pressure \( P_1 = 1.35 \text{ atm} \), initial temperature \( T_1 = 25 \degree C \), and final temperature \( T_2 = 355 \degree C \).

Convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature: \( T_1 = 25 + 273.15 \) and \( T_2 = 355 + 273.15 \).

Use the ideal gas law relationship for constant volume, which is \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \), where \( P_2 \) is the final pressure.

Rearrange the equation to solve for \( P_2 \): \( P_2 = P_1 \times \frac{T_2}{T_1} \).

Substitute the known values into the equation to find \( P_2 \).

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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 helps predict how gases behave under different conditions.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This means that as the temperature increases, the volume increases, and vice versa. In this scenario, since the volume is constant, we can use the relationship between temperature and pressure to find the new pressure after the temperature change.

Temperature Conversion

In gas law calculations, temperatures must be expressed in Kelvin rather than Celsius. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature. This is crucial because gas laws are derived based on absolute temperature, ensuring accurate calculations of pressure and volume changes.

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Textbook Question

Use the molar volume of a gas at STP to calculate the density (in g/L) of nitrogen gas at STP.

This picture represents a sample of gas at a pressure of 1 atm, a volume of 1 L, and a temperature of 25 °C. Draw a similar picture showing what would happen to the sample if the volume were reduced to 0.5 L and the temperature were increased to 250 °C. What would happen to the pressure?

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Textbook Question

A sample of N₂O gas has a density of 2.85 g/L at 298 K. What is the pressure of the gas (in mmHg)?

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Which gas sample has the greatest pressure? Assume that all the samples are at the same temperature. Explain.

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Textbook Question

What is the density (in g/L) of hydrogen gas at 20.0 °C and a pressure of 1655 psi?

Aerosol cans carry clear warnings against incineration because of the high pressures that can develop upon heating. Suppose that a can contains a residual amount of gas at a pressure of 755 mmHg and a temperature of 25 °C. What would the pressure be if the can were heated to 1155 °C?

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