A balloon contains 0.119 mol of gas and has a volume of 3.21 L. If an additional 0.103 mol of gas is added to the balloon (at constant temperature and pressure), what is its final volume?

검증된 단계별 안내

Identify the initial conditions: 0.119 mol of gas with a volume of 3.21 L.

Recognize that the problem involves the ideal gas law, where volume is directly proportional to the number of moles at constant temperature and pressure.

Calculate the total number of moles after adding the additional gas: 0.119 mol + 0.103 mol.

Set up the proportion using the initial and final conditions: \( \frac{V_1}{n_1} = \frac{V_2}{n_2} \), where \( V_1 = 3.21 \text{ L} \), \( n_1 = 0.119 \text{ mol} \), and \( n_2 \) is the total moles after addition.

Solve for \( V_2 \) to find the final volume of the balloon.

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주요 개념

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

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. This law allows us to predict how changes in the amount of gas will affect its volume when temperature and pressure are held constant.

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 means that if you add more moles of gas to a container, the volume will increase proportionally, assuming the temperature and pressure remain unchanged. This principle is crucial for solving problems involving changes in gas quantities.

Conservation of Volume in Gases

The conservation of volume in gases refers to the principle that, under constant temperature and pressure, the total volume of a gas mixture is the sum of the volumes of the individual gases. When additional gas is added to a balloon, the total volume can be calculated by adding the initial volume to the volume that corresponds to the added moles of gas, based on the Ideal Gas Law or Avogadro's Law.