The equation of state , corresponding to 8 g of `O_2` is

Options

A. `P V = 8 RT`
B. `PV = (RT)/(4)`
C. `P V = RT`
D. `P V = (RT)/(2)`

Answer

To find the equation of state corresponding to 8 g of \( O_2 \), we can use the ideal gas law, which is given by the equation:

\[ PV = nRT \]

where:
- \( P \) = pressure,
- \( V \) = volume,
- \( n \) = number of moles,
- \( R \) = universal gas constant,
- \( T \) = temperature in Kelvin.

### Step 1: Calculate the number of moles (\( n \))

The number of moles can be calculated using the formula:

\[ n = \frac{\text{mass}}{\text{molar mass}} \]

Given:
- Mass of \( O_2 = 8 \, \text{g} \)
- Molar mass of \( O_2 = 32 \, \text{g/mol} \)

Substituting the values:

\[ n = \frac{8 \, \text{g}}{32 \, \text{g/mol}} = \frac{1}{4} \, \text{mol} \]

### Step 2: Substitute \( n \) into the ideal gas law

Now, we substitute the value of \( n \) into the ideal gas law equation:

\[ PV = nRT \]

Substituting \( n = \frac{1}{4} \):

\[ PV = \left(\frac{1}{4}\right)RT \]

### Step 3: Rearrange the equation

We can rearrange the equation to isolate \( PV \):

\[ PV = \frac{RT}{4} \]

This is the equation of state corresponding to 8 g of \( O_2 \).

### Final Equation

Thus, the equation of state for 8 g of \( O_2 \) is:

\[ PV = \frac{RT}{4} \]