Question

A sample of 7.90 L of NH3 (ammonia) gas at 22 ∘C and 735 torr is bubbled into a 0.450 L solution of 0.400 M HCl (hydrochloric acid). The Kb value for NH3 is 1.8×10−5. Part A Assuming all the NH3 dissolves and that the volume of the solution remains at 0.450 L , calculate the pH of the resulting solution.

Answer 1

Answer: The pH of the solution is 9.14

Explanation:

• For ammonia:

To calculate the amount of hydrogen gas collected, we use the equation given by ideal gas which follows:

$PV=nRT$

where,

P = pressure of the gas = 735 torr

V = Volume of the gas = 7.90 L

T = Temperature of the gas = $22^oC=[22+273]K=295K$

R = Gas constant = $62.364\text{ L. torr }mol^{-1}K^{-1}$

n = number of moles of ammonia = ?

Putting values in above equation, we get:

$735torr\times 7.90L=n\times 62.364\text{ L. torr }mol^{-1}K^{-1}\times 295K\\\\n=\frac{735\times 7.90}{62.364\times 295}=0.316mol$

• For hydrochloric acid:

To calculate the number of moles for given molarity, we use the equation:

$\text{Molarity of the solution}=\frac{\text{Moles of solute}}{\text{Volume of solution (in L)}}$

Molarity of hydrochloric acid = 0.400 M

Volume of solution = 0.450 L

Putting values in above equation, we get:

$0.400M=\frac{\text{Moles of hydrochloric acid}}{0.450L}\\\\\text{Moles of hydrochloric acid}=(0.400\times 0.450)=0.18mol$

The chemical reaction for ethylamine and HCl follows the equation:

                   $NH_3+HCl\rightarrow NH_4Cl$

Initial:         0.316   0.18

Final:          0.136     -            0.18

Volume of the solution = 0.450 L

To calculate the pOH of basic buffer, we use the equation given by Henderson Hasselbalch:

$pOH=pK_b+\log(\frac{[salt]}{[base]})$

$pOH=pK_b+\log(\frac{[NH_4Cl]}{[NH_3]})$

We are given:

$pK_b$ = negative logarithm of base dissociation constant of ammonia = $-\log(1.8\times 10^{-5})=4.74$  

$[NH_4Cl]=\frac{0.18}{0.450}$

$[NH_3]=\frac{0.136}{0.450}$

pOH = ?

Putting values in above equation, we get:

$pOH=4.74+\log(\frac{0.18/0.450}{0.136/0.450})\\\\pOH=4.86$

To calculate pH of the solution, we use the equation:

$pH+pOH=14\\pH=14-4.86=9.14$

Hence, the pH of the solution is 9.14