The total pressure exerted by the mixture of equal moles of two gases is `5xx10^(3) Nm^(-2)` in a container of volume 2 litres at 273 K. Calculate the number of the gases mixed.

Explanation

To solve the problem, we will use the ideal gas equation, which is given by:

\[ PV = nRT \]

Where:
- \( P \) = Pressure (in Pascals)
- \( V \) = Volume (in cubic meters)
- \( n \) = Number of moles of gas
- \( R \) = Universal gas constant (8.314 J/(mol·K))
- \( T \) = Temperature (in Kelvin)

### Step 1: Identify the given values
- Total pressure, \( P = 5 \times 10^3 \, \text{N/m}^2 \)
- Volume, \( V = 2 \, \text{liters} = 2 \times 10^{-3} \, \text{m}^3 \) (conversion from liters to cubic meters)
- Temperature, \( T = 273 \, \text{K} \)
- Gas constant, \( R = 8.314 \, \text{J/(mol·K)} \)

### Step 2: Rearrange the ideal gas equation to solve for \( n \)
We need to find the number of moles \( n \). Rearranging the ideal gas equation gives us:

\[ n = \frac{PV}{RT} \]

### Step 3: Substitute the values into the equation
Now, we will substitute the known values into the rearranged equation:

\[ n = \frac{(5 \times 10^3) \times (2 \times 10^{-3})}{(8.314) \times (273)} \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:

\[ 5 \times 10^3 \times 2 \times 10^{-3} = 10 \]

Calculating the denominator:

\[ 8.314 \times 273 \approx 2270.622 \]

### Step 5: Perform the division to find \( n \)
Now we can calculate \( n \):

\[ n = \frac{10}{2270.622} \approx 0.0044 \, \text{moles} \]

### Step 6: Determine the number of gases mixed
Since the problem states that the mixture consists of equal moles of two gases, we can conclude that the total number of moles of gases mixed is:

\[ \text{Total number of gases} = 2 \times n = 2 \times 0.0044 \approx 0.0088 \, \text{moles} \]

However, since we are looking for the number of different gases mixed, the answer is simply 2.

### Final Answer
The number of gases mixed is **2**.

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