A cylinder with a moveable piston contains 0.221 mol of gas and has a volume of 178 mL. What is its volume if an additional 0.244 mol of gas is added to the cylinder? (Assume constant temperature and pressure.)

검증된 단계별 안내

Identify the initial and final conditions of the gas. Initially, you have 0.221 mol of gas with a volume of 178 mL. After adding 0.244 mol, the total amount of gas becomes 0.221 mol + 0.244 mol.

Use Avogadro's Law, which states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. This can be expressed as V1/n1 = V2/n2, where V1 and n1 are the initial volume and moles, and V2 and n2 are the final volume and moles.

Substitute the known values into the Avogadro's Law equation: (178 \(\text{ mL}\)) / (0.221 \(\text{ mol}\)) = V2 / (0.221 \(\text{ mol}\) + 0.244 \(\text{ mol}\)).

Solve the equation for V2, which represents the final volume of the gas after the additional moles are added.

Ensure the units are consistent and check your work to confirm that the relationship between moles and volume is correctly applied.

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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. In this scenario, since temperature and pressure are constant, the relationship between the number of moles and volume can be simplified, allowing us to determine how the volume changes with the addition of more gas.

Avogadro's Law

Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present. This principle is crucial for solving the problem, as it allows us to predict how the volume will increase when additional moles of gas are added to the cylinder.

Conservation of Volume

In a closed system with a moveable piston, the total volume can change as gas is added or removed. The conservation of volume principle indicates that the volume of the gas will adjust to accommodate the new amount of gas while maintaining constant temperature and pressure, which is essential for calculating the new volume after adding more moles.