Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O 2 gas at a pressure of 16,500 kPa at 23 °C. (a) What mass of O 2 does the tank contain?

First, use the ideal gas law equation to find the number of moles of O2 gas in the tank. The ideal gas law is given by: PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: T=23+273.15.. Rearrange the ideal gas law equation to solve for n (number of moles): n=PVRT. Use the given values: P = 16,500 kPa, V = 210.0 L, and the converted temperature in Kelvin. Use the ideal gas constant R = 8.314 J/(mol·K) and convert pressure to Pa (1 kPa = 1000 Pa) if necessary.. Calculate the number of moles of O2 using the rearranged equation and the converted values.. Finally, convert the number of moles of O2 to mass. Use the molar mass of O2, which is approximately 32.00 g/mol. Multiply the number of moles by the molar mass to find the mass of O2 in grams.

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (a) What mass of O2 does the tank contain?

First, use the ideal gas law equation to find the number of moles of O2 gas in the tank. The ideal gas law is given by: PV=nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: T=23+273.15. Rearrange the ideal gas law equation to solve for n (number of moles): n=PVRT. Use the given values: P = 16,500 kPa, V = 210.0 L, and the converted temperature in Kelvin. Use the ideal gas constant R = 8.314 J/(mol·K) and convert pressure to Pa (1 kPa = 1000 Pa) if necessary. Calculate the number of moles of O2 using the rearranged equation and the converted values. Finally, convert the number of moles of O2 to mass. Use the molar mass of O2, which is approximately 32.00 g/mol. Multiply the number of moles by the molar mass to find the mass of O2 in grams.

Ch.10 - Gases

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Brown 14th Edition

Ch.10 - Gases

문제 44a

10장, 문제 44a

Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O₂ gas at a pressure of 16,500 kPa at 23 °C. (a) What mass of O₂ does the tank contain?

검증된 단계별 안내

First, use the ideal gas law equation to find the number of moles of O2 gas in the tank. The ideal gas law is given by:

P V = n R T

, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature:

T = 23 + 273.15

Rearrange the ideal gas law equation to solve for n (number of moles):

n = \frac{P V}{R T}

. Use the given values: P = 16,500 kPa, V = 210.0 L, and the converted temperature in Kelvin. Use the ideal gas constant R = 8.314 J/(mol·K) and convert pressure to Pa (1 kPa = 1000 Pa) if necessary.

Calculate the number of moles of O2 using the rearranged equation and the converted values.

Finally, convert the number of moles of O2 to mass. Use the molar mass of O2, which is approximately 32.00 g/mol. Multiply the number of moles by the molar mass to find the mass of O2 in grams.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the amount of gas in a given volume and pressure, allowing us to determine the number of moles of O2 in the tank.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For O2, the molar mass is approximately 32.00 g/mol. Knowing the molar mass is crucial for converting the number of moles of O2 obtained from the Ideal Gas Law into grams, which answers the question about the mass of gas in the tank.

Unit Conversion

Unit conversion is the process of converting one unit of measurement to another. In this context, it is important to convert pressure from kPa to atm or other relevant units if necessary, and to ensure that all units are consistent when applying the Ideal Gas Law. This ensures accurate calculations and results.