Correct gas equation is :

Options

A. `(V_(1)T_(2))/(p_(1))=(V_(2)T_(1))/(p_(2))`
B. `(p_(1)T_(1))/(V_(1))=(p_(2)V_(2))/(T_(2))`
C. `(p_(1)V_(1))/(p_(2)V_(2))=(T_(1))/(T_(2))`
D. `(V_(1)V_(2))/(T_(1)T_(2))=p_(1)p_(2)`

Explanation

To solve the question regarding the correct gas equation, we will derive the relationship using the ideal gas law and compare the given options.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is temperature.

2. **Set Up the Equations for Two Gases**:
For gas 1, we can write:
\[ P_1 V_1 = n R T_1 \]
For gas 2, we can write:
\[ P_2 V_2 = n R T_2 \]

3. **Assume the Number of Moles is the Same**:
We assume that the number of moles \(n\) is the same for both gases. This means we can cancel \(n\) and \(R\) when we divide the two equations.

4. **Divide the Two Equations**:
Dividing the equation for gas 1 by the equation for gas 2, we get:
\[ \frac{P_1 V_1}{P_2 V_2} = \frac{T_1}{T_2} \]

5. **Rearranging the Equation**:
Rearranging the above equation gives us:
\[ P_1 V_1 T_2 = P_2 V_2 T_1 \]

6. **Identifying the Correct Expression**:
Now, we need to compare this derived equation with the options provided in the question. The derived equation can be rearranged to show the relationship between the variables.

7. **Conclusion**:
The correct expression derived from the ideal gas law is:
\[ \frac{P_1 V_1}{P_2 V_2} = \frac{T_1}{T_2} \]
Thus, the correct option from the given choices is **Option A**.