Question

At 12 °C and 750 mm Hg pressure, the volume of a gas is 200 cm³. What will be its volume at 40°C and 720 mm Hg pressure?

Answer 1

✯ Volume = 228.8 cm³ ✯

Explanation:

Given:

• $\sf{T_1= (12+273)=285\:K}$
• $\sf{p_1=750\:mm\:Hg=75\:cm\:Hg}$
• $\sf{V_1=200\:cm^3}$
• $\sf{T_2=(40+273)=313\:K}$
• $\sf{p_2=720\:mm\:Hg=72\:cm\:Hg}$

To find:

• Volume $\sf{(V_2)}$ at 40°C and 720 mm Hg pressure.

Solution:

We know that,

${\boxed{\sf{\dfrac{p_1\:V_1}{T_1}=\dfrac{p_2\:V_2}{T_2}}}}$

• [ Put values]

$\implies\sf{\dfrac{75\times\:200}{285}=\dfrac{72\times\:V_2}{313}}$

$\implies\sf{\dfrac{15000}{285}=\dfrac{72V_2}{313}}$

$\implies\sf{285\times\:72V_2=15000\times\:313}$

$\implies\sf{20520V_2=4695000}$

$\implies\sf{V_2=228.8}$

Therefore, the volume is 228.8 cm³.

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More info -

• Boyle's law = $\sf{p_1V_1=p_2V_2=p_3V_3=.....=Constant}$

• Charles' law = $\sf{\dfrac{V_1}{V_2}=\dfrac{T_1}{T_2}}$