A cylinder with a moveable piston contains 0.553 mol of gas and has a volume of 253 mL. What is its volume if an additional 0.365 mol of gas is added to the cylinder? (Assume constant temperature and pressure.)

Verified step by step guidance

1. Identify the initial conditions and the final conditions. Initially, there are 0.553 mol of gas in a volume of 253 mL.
2. Determine the total amount of gas after adding 0.365 mol to the initial amount. This is done by summing up the initial moles and the additional moles.
3. Use the direct proportionality of moles and volume under constant temperature and pressure (Avogadro's Law), which states that the volume of a gas is directly proportional to the number of moles of the gas when temperature and pressure are held constant.
4. Set up a proportion based on Avogadro's Law: \( \frac{V_1}{n_1} = \frac{V_2}{n_2} \), where \(V_1\) and \(n_1\) are the initial volume and number of moles, and \(V_2\) and \(n_2\) are the final volume and total number of moles.
5. Solve the proportion for \(V_2\) to find the new volume of the gas in the cylinder.

Key Concepts

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 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 more 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 occupied by the gas will adjust according to the number of moles present, provided that temperature and pressure remain constant, which is essential for calculating the new volume after adding gas.