A vessel is filled with a gas at a pressure of 76 cm of mercury at a certain temperature. The mass of the gas is increased by 50% by introducing more gas in the vessel at the same temperature. Find the resultant pressure of the gas. a) 76 cm of mercury b) 108 cm of mercury c) 112 cm mercury d) 114 cm of mercury

Options

A. 76 cm of mercury
B. 108 cm of mercury
C. 112 cm mercury
D. 114 cm of mercury

Explanation

To find the resultant pressure of the gas after increasing its mass by 50%, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Pressure**:
The initial pressure \( P_1 \) of the gas is given as 76 cm of mercury.

\[ P_1 = 76 \, \text{cm of mercury} \]

2. **Understand the Relationship Between Pressure and Mass**:
According to the kinetic theory of gases, at constant temperature and volume, the pressure exerted by a gas is directly proportional to its mass. This can be expressed as:

\[ \frac{P_2}{P_1} = \frac{m_2}{m_1} \]

where \( P_2 \) is the final pressure, \( P_1 \) is the initial pressure, \( m_2 \) is the final mass, and \( m_1 \) is the initial mass.

3. **Calculate the Final Mass**:
The mass of the gas is increased by 50%. Therefore, the final mass \( m_2 \) can be calculated as:

\[ m_2 = m_1 + 0.5 \times m_1 = 1.5 \times m_1 \]

4. **Substitute the Mass Relationship into the Pressure Equation**:
Now, substituting \( m_2 \) into the pressure equation gives:

\[ \frac{P_2}{P_1} = \frac{1.5 \times m_1}{m_1} \]

This simplifies to:

\[ \frac{P_2}{P_1} = 1.5 \]

5. **Calculate the Final Pressure**:
Now we can find \( P_2 \):

\[ P_2 = 1.5 \times P_1 = 1.5 \times 76 \, \text{cm of mercury} \]

Performing the multiplication:

\[ P_2 = 114 \, \text{cm of mercury} \]

6. **Conclusion**:
The resultant pressure of the gas after increasing its mass by 50% is:

\[ P_2 = 114 \, \text{cm of mercury} \]

### Final Answer:
The correct option is **d) 114 cm of mercury**.