A graph is plotted with PV/T on y-axis and mass of the gas along x-axis for different gases. The graph is

Options

A. A) a straight line paralled to x-axis for all the gases
B. B) a straight line passing through origin with a slope having a constant value for all the gases
C. C) a straight line passing through origin with a slope having different value for different gases
D. D) a straight line parallel to y-axis for all the gases

Answer

To solve the problem, we need to analyze the relationship between the pressure (P), volume (V), temperature (T), and mass (m) of different gases. The question states that we are plotting \( \frac{PV}{T} \) on the y-axis against the mass of the gas on the x-axis.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

2. **Relate Moles to Mass**:
The number of moles \( n \) can be expressed in terms of mass \( m \) and molar mass \( M \):
\[ n = \frac{m}{M} \]
Substituting this into the ideal gas law gives:
\[ PV = \frac{m}{M} RT \]

3. **Rearranging the Equation**:
Dividing both sides by \( T \) gives:
\[ \frac{PV}{T} = \frac{mR}{M} \]

4. **Identifying the Graph**:
From the equation \( \frac{PV}{T} = \frac{mR}{M} \), we can see that \( \frac{PV}{T} \) is directly proportional to the mass \( m \) of the gas, with the slope being \( \frac{R}{M} \). This means that if we plot \( \frac{PV}{T} \) on the y-axis and mass \( m \) on the x-axis, we will get a straight line.

5. **Slope of the Line**:
The slope of this line is given by \( \frac{R}{M} \), which varies for different gases because the molar mass \( M \) is different for different gases.

6. **Conclusion**:
Therefore, the graph of \( \frac{PV}{T} \) versus mass \( m \) will be a straight line passing through the origin, with a slope that depends on the molar mass of the gas.

### Final Answer:
The graph is a straight line passing through the origin with different slopes for different gases.