The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be

Options

A. `PV=(5/32)RT`
B. PV=5RT
C. `PV=(5/2)RT`
D. `PV=(5/16)RT`

Answer

To find the equation of state for 5 g of oxygen (O₂) at a pressure P and temperature T occupying a volume V, we can use the ideal gas law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant (approximately \( 8.314 \, \text{J/(mol K)} \))
- \( T \) = temperature in Kelvin

### Step-by-Step Solution:

1. **Determine the molar mass of oxygen (O₂)**:
- The molar mass of oxygen (O₂) is approximately 32 g/mol.

2. **Calculate the number of moles (n)**:
- The number of moles of oxygen can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{5 \, \text{g}}{32 \, \text{g/mol}} = \frac{5}{32} \, \text{mol} \]

3. **Substitute the value of n into the ideal gas law**:
- Now that we have \( n \), we can substitute it into the ideal gas equation:
\[ PV = nRT \]
- Replacing \( n \) with \( \frac{5}{32} \):
\[ PV = \left(\frac{5}{32}\right)RT \]

4. **Final equation**:
- The equation of state for 5 g of oxygen at pressure \( P \), temperature \( T \), and volume \( V \) is:
\[ PV = \frac{5}{32}RT \]