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

Options

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

Explanation

To find the equation of state for 5 g of oxygen at pressure P, temperature T, and volume V, we will use the ideal gas equation and the concept of moles. Here’s a step-by-step solution:

### Step 1: Write the Ideal Gas Equation
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Calculate the Number of Moles
To find the number of moles \( n \), we use the formula:
\[ n = \frac{\text{Total Mass}}{\text{Molar Mass}} \]

Given:
- Total mass of oxygen = 5 g
- Molar mass of oxygen (O₂) = 32 g/mol (since the atomic mass of oxygen is 16 g/mol and there are 2 atoms in O₂).

Thus,
\[ n = \frac{5 \text{ g}}{32 \text{ g/mol}} \]

### Step 3: Substitute the Number of Moles into the Ideal Gas Equation
Now we substitute the value of \( n \) back into the ideal gas equation:
\[ PV = \left(\frac{5}{32}\right)RT \]

### Step 4: Rearranging the Equation
This gives us the equation of state for the gas:
\[ PV = \frac{5}{32} RT \]

### Final Expression
Thus, the equation of state for 5 g of oxygen at pressure \( P \), temperature \( T \), and volume \( V \) is:
\[ PV = \frac{5}{32} RT \]