Question

250 cm3 of nitrogen at 720mm pressure is mixed with 380 cm3 of oxygen
at 650mm pressure in Idm3 vessel at constant temperature. What will
be the total pressure of the gas mixture ?​

Answer 1

Answer:

This will be solved using Boyle's law and Dalton's law of partial pressures.

At constant temperature:

pV = p'V' (Boyle's law)

where p and V are partial pressure and volume of a gas respectively. p' is the partial pressure of the same gas at a different volume V'.

First we need to calculate the partial pressures of both the gases in the mixture which is 1 L (1000 mL).

For nitrogen:

 

pN2×1000 mL=720 mm Hg×250 mL⇒pN2=180 mm Hg

Similarly for oxygen:

pO2×1000 mL=650 mm Hg×380 mL⇒pO2=247 mm Hg

Now, we have the partial pressures of both the gases in the mixture. So, we can now easily find the total pressure of the mixture using Dalton's law of partial pressures, according to which it will be the sum of partial pressures of the individual gases. Thus,

pmixture=pN2+pO2⇒pmixture=180+247⇒pmixture=427 mm Hg

Answer 2

The total pressure of the gas mixture is 427 mm. Explanation:

Given that,

Volume of nitrogen = 250 cm³

Pressure = 720 mm

Volume of oxygen = 380 cm³

Volume of vessel $V_{v}= 1 cm^3$

We need to calculate the pressure of nitrogen

Using formula of Boyle's law

$PV=P'V'$

$P_{N}=\dfrac{P_{m}V_{N}}{V_{v}}$

Put the value into the formula  

$P_{N}=\dfrac{720\times250}{1000}$

$P_{N}=180\ mm$

We need to calculate the pressure of oxygen

Using formula of pressure  

$P_{o}=\dfrac{P_{m}V_{o}}{V_{v}}$  

Put the value into the formula  

$P_{o}=\dfrac{650\times380}{1000}$

$P_{o}=247\ mm$

We need to calculate the total pressure of the gas mixture

Using formula of pressure

$P=P_{N}+P_{o}$

Put the value into the formula

$P=180+247$

$P=427\ mm$

Hence, The total pressure of the gas mixture is 427 mm.

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Topic : pressure

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