Which of the following relationships between partial pressure , volume and temperature is correct ?
(i) `P = (nRT)/(V)`
(ii) `P_("total") = P_(1) + P_(2) + P_(3)`
(iii) `P_("total") = (n_(1) + n_(2) + n_(3)) (RT)/(V)`

Options

A. (i) and (ii)
B. (i) and (iii)
C. (ii) and (iii)
D. (i) , (ii) and (iii)

Answer

To solve the question regarding the relationships between partial pressure, volume, and temperature, we will analyze each of the given equations step by step.

### Step 1: Analyze the First Equation
The first equation given is:

\[ P = \frac{nRT}{V} \]

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

**Conclusion**: This equation is correct.

### Step 2: Analyze the Second Equation
The second equation given is:

\[ P_{\text{total}} = P_1 + P_2 + P_3 \]

This is known as Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas in the mixture.

**Conclusion**: This equation is also correct.

### Step 3: Analyze the Third Equation
The third equation given is:

\[ P_{\text{total}} = \frac{(n_1 + n_2 + n_3)RT}{V} \]

Here, we can derive this equation from the ideal gas law. If we consider three gases with moles \( n_1, n_2, \) and \( n_3 \), the total number of moles \( n_{\text{total}} \) is:

\[ n_{\text{total}} = n_1 + n_2 + n_3 \]

Substituting \( n_{\text{total}} \) into the ideal gas equation gives:

\[ P_{\text{total}} = \frac{n_{\text{total}}RT}{V} = \frac{(n_1 + n_2 + n_3)RT}{V} \]

**Conclusion**: This equation is also correct.

### Final Conclusion
All three equations are correct relationships between partial pressure, volume, and temperature. Therefore, the answer to the question is that all the given relationships are correct.