Question

If 3.0 atm of pure HN3(g) is decomposed initially, what is the final total pressure in the reaction container? What are the partial pressures of nitrogen and hydrogen gas? Assume the volume and temperature of the reaction container are constant.

Answer 1

This is an incomplete question, here is a complete question.

Hydrogen azide, HN₃, decomposes on heating by thefollowing unbalanced reaction:

$HN_3(g)\rightarrow N_2(g)+H_2(g)$

If 3.0 atm of pure HN₃ (g) is decomposed initially,what is the final total pressure in the reaction container? Whatare the partial pressures of nitrogen and hydrogen gas? Assume thatthe volume and temperature of the reaction container are constant.

Answer : The partial pressure of $N_2$ and $H_2$ gases are, 4.5 atm and 1.5 atm respectively.

Explanation :

The given unbalanced chemical reaction is:

$HN_3(g)\rightarrow N_2(g)+H_2(g)$

This reaction is an unbalanced chemical reaction because in this reaction number of hydrogen and nitrogen atoms are not balanced on both side of the reaction.

In order to balance the chemical equation, the coefficient '2' put before the $HN_3$ and the coefficient '3' put before the $N_2$ then we get the balanced chemical equation.

The balanced chemical reaction will be,

$2HN_3(g)\rightarrow 3N_2(g)+H_2(g)$

As we are given:

The pressure of pure $HN_3$ = 3.0 atm

$p_{Total}=2\times p_{HN_3}=2\times 3.0atm=6.0atm$

From the reaction we conclude that:

Number of moles of $N_2$ = 3 mol

Number of moles of $H_2$ = 1 mol

Now we have to calculate the mole fraction of $N_2$ and $H_2$

$\text{Mole fraction of }N_2=\frac{\text{Moles of }N_2}{\text{Moles of }N_2+\text{Moles of }H_2}=\frac{3}{3+1}=0.75$

and,

$\text{Mole fraction of }H_2=\frac{\text{Moles of }H_2}{\text{Moles of }N_2+\text{Moles of }H_2}=\frac{1}{3+1}=0.25$

Now we have to calculate the partial pressure of $N_2$ and $H_2$

According to the Raoult's law,

$p_i=X_i\times p_T$

where,

$p_i$ = partial pressure of gas

$p_T$ = total pressure of gas  = 6.0 atm

$X_i$ = mole fraction of gas

$p_{N_2}=X_{N_2}\times p_T$

$p_{N_2}=0.75\times 6.0atm=4.5atm$

and,

$p_{H_2}=X_{H_2}\times p_T$

$p_{H_2}=0.25\times 6.0atm=1.5atm$

Thus, the partial pressure of $N_2$ and $H_2$ gases are, 4.5 atm and 1.5 atm respectively.