Question

A cylindrical vessel contains 16 kg at 1 atm. A certain amount of substance is taken out so that pressure becomes 0.7 atm. Find the amount taken out (in kg).

• A. 2.5 kg
• B. 3.5 kg
• C. 4 kg
• D. 5 kg

Hint:

When pressure is reduced, the amount of substance (mass) is directly proportional to the pressure. Use the ideal gas law to find the relationship between initial and final conditions.

Answer 1

The Correct Option is B

We are given that the initial mass of the substance is 16 kg at 1 atm pressure, and the pressure is reduced to 0.7 atm. We are asked to find the amount of substance taken out.

1. Step 1: Use the ideal gas law relation According to the ideal gas law, \( PV = nRT \), where: - \( P \) is the pressure, - \( V \) is the volume, - \( n \) is the number of moles, - \( R \) is the gas constant, - \( T \) is the temperature. Since the temperature and volume remain constant, the relationship between pressure and mass is: \[ \frac{P_1}{P_2} = \frac{m_1}{m_2} \] where: - \( P_1 = 1 \) atm, - \( P_2 = 0.7 \) atm, - \( m_1 = 16 \) kg (initial mass), - \( m_2 \) is the final mass.

2. Step 2: Solve for the final mass \( m_2 \): Using the formula: \[ \frac{1}{0.7} = \frac{16}{m_2} \] Solving for \( m_2 \): \[ m_2 = \frac{16 \times 0.7}{1} = 1
1.2 \, \text{kg} \]

3. Step 3: Find the amount taken out: The amount of substance taken out is: \[ 16 - 1
1.2 =
3.5 \, \text{kg} \] Thus, the amount taken out is \(
3.5 \) kg.