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, R is the ideal gas constant, and T is temperature in Kelvin.

Step-by-Step Calculation

1. Convert Temperature to Kelvin

The temperature given is 27°C. To convert this to Kelvin, we add 273.15:

T = 27 + 273.15 = 300.15 K

2. Identify the Volume

The volume of the container is provided as 10 L.

3. Calculate Total Moles of Gas

Initially, we have 2 moles of NH₃ and 1 mole of HCl. However, when these gases react, they form ammonium chloride (NH₄Cl) according to the reaction:

• NH₃(g) + HCl(g) → NH₄Cl(s)

In this reaction, 1 mole of NH₃ reacts with 1 mole of HCl to produce 1 mole of NH₄Cl, which is a solid and does not contribute to the gas pressure. Therefore, after the reaction, we will have:

• 2 moles of NH₃ - 1 mole of NH₃ = 1 mole of NH₃ remaining
• 1 mole of HCl - 1 mole of HCl = 0 moles of HCl remaining

Thus, we are left with 1 mole of NH₃ in the gas phase.

4. Apply the Ideal Gas Law

Now we can use the ideal gas law to find the pressure:

• P = (nRT) / V

Substituting the values:

• n = 1 mole (remaining NH₃)
• R = 0.0821 L·atm/(K·mol) (ideal gas constant)
• T = 300.15 K
• V = 10 L

Now, plug in the values:

P = (1 mol × 0.0821 L·atm/(K·mol) × 300.15 K) / 10 L

P = (24.726615) / 10

P = 2.4726615 atm

Final Result

Rounding to three significant figures, the pressure in the container will be approximately 2.47 atm.

This calculation illustrates how chemical reactions can affect the number of moles of gas present and, consequently, the pressure in a closed system. In this case, the reaction between NH₃ and HCl reduced the total number of gas moles, leading to a specific pressure that can be calculated using the ideal gas law.