For 8g of helium gas (assume ideal behaviour), what is the slope of the straight line in PV VS T graph 

Options

A. 1 lt. atm. `K^(-1)`
B. 0.0821 lt. atm. `K^(-1)`
C. 0.1642 lt. atm .`K^(-1)`
D. 2 lt. atm . `K^(-1)`

Explanation

To find the slope of the straight line in the PV vs T graph for 8g of helium gas, we can follow these steps:

### Step-by-Step Solution:

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

2. **Rearranging the Equation**: We can rearrange the ideal gas law to express \( PV \) in terms of \( T \):
\[ PV = nRT \]
This implies that if we plot \( PV \) on the y-axis and \( T \) on the x-axis, the slope of the line will be:
\[ \text{slope} = \frac{PV}{T} = nR \]

3. **Calculate the Number of Moles (n)**: The number of moles can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
For helium, the molar mass is 4 g/mol. Given that the mass of helium is 8 g:
\[ n = \frac{8 \, \text{g}}{4 \, \text{g/mol}} = 2 \, \text{mol} \]

4. **Use the Universal Gas Constant (R)**: The value of the universal gas constant \( R \) in liter-atm per mole per Kelvin is:
\[ R = 0.0821 \, \text{L atm/(mol K)} \]

5. **Calculate the Slope**: Now, substituting the values of \( n \) and \( R \) into the slope formula:
\[ \text{slope} = nR = 2 \, \text{mol} \times 0.0821 \, \text{L atm/(mol K)} = 0.1642 \, \text{L atm/K} \]

6. **Final Answer**: Therefore, the slope of the straight line in the PV vs T graph for 8 g of helium gas is:
\[ \text{slope} = 0.1642 \, \text{L atm/K} \]

### Conclusion:
The correct answer is \( 0.1642 \, \text{L atm/K} \).