2 mol of NH₃ and 1 mol of HCl are introduced into a 10 L evacuated container at 27 C. the pressure set up in the container will be?

To determine the pressure in the container after introducing 2 moles of ammonia (NH₃) and 1 mole of hydrochloric acid (HCl), we can use the ideal gas law, which is expressed as PV = nRT. In this equation, P represents pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

Step-by-Step Calculation

1. Convert Temperature to Kelvin

First, we need to convert the temperature from Celsius to Kelvin. The formula for this conversion is:

T(K) = T(°C) + 273.15

For our case:

T = 27 + 273.15 = 300.15 K

2. Calculate Total Moles of Gas

Next, we need to find the total number of moles of gas present in the container. We have:

• 2 moles of NH₃
• 1 mole of HCl

Thus, the total moles (n) = 2 + 1 = 3 moles.

3. Use the Ideal Gas Constant

The ideal gas constant (R) can be expressed in various units. For our calculations, we will use:

R = 0.0821 L·atm/(K·mol)

4. Apply the Ideal Gas Law

Now we can substitute the values into the ideal gas law equation:

PV = nRT

We need to solve for P (pressure):

P = nRT / V

Substituting the known values:

• n = 3 moles
• R = 0.0821 L·atm/(K·mol)
• T = 300.15 K
• V = 10 L

Now, plugging in the numbers:

P = (3 moles) × (0.0821 L·atm/(K·mol)) × (300.15 K) / (10 L)

5. Perform the Calculation

Calculating this gives:

P = (3 × 0.0821 × 300.15) / 10

P = (73.56) / 10

P = 7.356 atm

Final Result

The pressure set up in the container will be approximately 7.36 atm.

Considerations

It's important to note that this calculation assumes ideal behavior of the gases involved. In real-world scenarios, deviations may occur due to factors like intermolecular forces and the volume occupied by the gas molecules themselves, especially at high pressures or low temperatures. However, for many practical purposes, the ideal gas law provides a good approximation.