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 derive the equation of state for 5 g of oxygen at a pressure \( P \) and temperature \( T \), occupying a volume \( V \), we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The ideal gas law 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
- \( T \) = temperature of the gas in Kelvin

### Step 2: Calculate the Number of Moles
We are given the mass of oxygen, \( m = 5 \) grams. To find the number of moles \( n \), we use the formula:
\[ n = \frac{m}{M} \]
where \( M \) is the molar mass of oxygen. The molar mass of oxygen (O₂) is approximately \( 32 \) grams per mole.

Substituting the values:
\[ n = \frac{5 \text{ g}}{32 \text{ g/mol}} = \frac{5}{32} \text{ moles} \]

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

### Step 4: Rearranging the Equation
To express the equation in a standard form, we can rearrange it:
\[ PV = \frac{5}{32}RT \]

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

### Conclusion
The correct option from the given choices is option 1:
\[ PV = \frac{5}{32}RT \]

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