Question

The total pressure of a gaseous mixture of 2.8g of n^2, 3.2 g of o^2 and o.5 g of h^2 is 4.5atm. calculate the partial pressure of h^2 gas

Answer 1

$\huge {\bold {\underline {\underline{Given : - }}}}$

• Total pressure = 4.5 atm
• Amount of gases present in mixture are 2.8g of N₂ , 3.2 g of O₂ and 0.5g of H₂

$\huge {\bold {\underline {\underline{To \: find: - }}}}$

• Partial pressure of H₂ gas

$\huge {\bold {\underline {\underline{Solution : - }}}}$

Number of moles of a substance is given by ,

$\large \rm {\underline {\bold {\boxed {\bigstar{ \: | n = \dfrac{given \: weight}{gram \: atomic \: weight} }}}}}$

a] Given weight of N₂ = 2.8g

Atomic weight of N₂ = 28g

Number of moles of N₂ is ,

$: \implies \: ({n})_{N_2} = \frac{2.8}{28} \\ \\ : \implies {\bold {\boxed {\pink {(n)_{N_2} = 0.1}}}}$

b] Given weight of O₂ = 3.2 g

Atomic weight of O₂ = 32g

$: \implies (n)_{o_2} = \frac{3.2}{32} \\ \\ : \implies {\bold {\boxed {\pink {(n)_{o_2} = 0.1}}}}$

c] Given weight of H₂ = 0.5 g

Atomic weight of H₂ = 2

$: \implies \: (n)_{H_2} = \frac{0.5}{2} \\ \\ : \implies {\bold {\boxed {\pink{(n)_{H_2} = 0.25}}}}$

Total number of moles in the given mixture = 0.1 + 0.1 + 0.25 = 0.45 mol

Mole fraction of the first gas in the mixture is given by,

$\large{\bold {\underline {\boxed {\bigstar{ \: | m = \dfrac{number \: of \: moles \: of \: the \: first \: gas}{total \: number \: of \: moles \: in \: the \: mixture} }}}}}$

Mole fraction of H₂ is ,

$: \implies \: (m)_{H_2} = \dfrac{0.25}{0.45} \\ \\ : \implies {\bold {\boxed {\pink{ (m)_{H_2} = 0.5}}}}$

We have ,

• Mole fraction of H₂ = 0.5
• Total pressure in the mixture = 4.5 atm

Partial pressure of any gas in the mixture is given by,

$\large \rm{\underline {\bold {\boxed {\bigstar{ | p = m \times \:P }}}}}$

Where ,

• p is partial pressure
• m is mole fraction of the certain gas
• P is total pressure in the mixture

Partial pressure of H₂ is ,

$: \implies \: (p)_{H_2} = 0.5 \times 4.5 \\ \\ : \implies \: (p)_{H_2} = 2.25 \: atm$

∴ The partial pressure of H₂ in the given mixture is 2.25 atm