A balloon contains 0.158 mol of gas and has a volume of 2.46 L. If an additional 0.113 mol of gas is added to the balloon (at the same temperature and pressure), what is its final volume?

검증된 단계별 안내

Identify the initial conditions: 0.158 mol of gas with a volume of 2.46 L.

Recognize that the problem involves the ideal gas law, which can be expressed as \( PV = nRT \).

Since temperature and pressure are constant, use the relationship \( \frac{V_1}{n_1} = \frac{V_2}{n_2} \) to find the final volume.

Calculate the total moles of gas after adding 0.113 mol: \( n_2 = 0.158 + 0.113 \).

Use the proportion \( \frac{2.46}{0.158} = \frac{V_2}{n_2} \) to solve for the final volume \( V_2 \).

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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, provided temperature and pressure remain constant.

Avogadro's Principle

Avogadro's Principle states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. This principle implies that the volume of a gas is directly proportional to the number of moles of gas present, allowing us to calculate the change in volume when additional moles of gas are added to a system.

Volume and Moles Relationship

The relationship between volume and moles of a gas is crucial for solving gas-related problems. According to Avogadro's Principle, if the temperature and pressure are constant, adding more moles of gas will increase the volume proportionally. Therefore, to find the final volume after adding gas, one can simply calculate the total number of moles and apply the Ideal Gas Law to determine the new volume.