(A) Given: $V = 1 \, dm^3 = 1 \, L$,$T = -23 \, ^\circ C = 250 \, K$,$P = 7.6 \times 10^{-5} \, torr = \frac{7.6 \times 10^{-5}}{760} \, atm = 10^{-7}

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(A) Given: $V = 1 \, dm^3 = 1 \, L$,$T = -23 \, ^\circ C = 250 \, K$,$P = 7.6 \times 10^{-5} \, torr = \frac{7.6 \times 10^{-5}}{760} \, atm = 10^{-7} \, atm$. Using the ideal gas equation $PV = nRT$,we find the number of moles $n$: $n = \frac{PV}{RT} = \frac{10^{-7} \times 1}{0.0821 \times 250} \approx 4.87 \times 10^{-9} \, mol$. The number of molecules $N = n \times N_A$: $N = 4.87 \times 10^{-9} \times 6.022 \times 10^{23} \approx 2.93 \times 10^{15}$ molecules.

Class 11 Chemistry States of Matter Ideal gas equation and Related gas laws

Medium

$A$ vacuum vessel of volume $1 \, dm^3$ is evacuated at a constant temperature of $-23 \, ^\circ C$ until the pressure drops to $7.6 \times 10^{-5} \, torr$. What is the number of molecules remaining in the vessel?

A
$2.9 \times 10^{15}$
B
$1.56 \times 10^{16}$
C
$1.56 \times 10^{16}$
D
$2.9 \times 10^{20}$

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States of Matter

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Ideal gas equation and Related gas laws

Calculate the temperature of $2 \text{ moles}$ of gas occupying a volume of $5.0 \text{ L}$ at a pressure of $24.6 \text{ atm}$. (Given: $R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}$) (in $^\circ \text{C}$)

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Medium

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If $4 \ g$ of $O_2$ and $2 \ g$ of $H_2$ are filled in a $1 \ L$ bulb at $0 \ ^oC$,the total pressure of the mixture will be...... (in $atm$)

Medium

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$A$ gas at a pressure of $2 \ atm$ is heated from $25^{\circ} C$ to $323^{\circ} C$ and simultaneously compressed to $\frac{2}{3}$ of its original volume. What is the final pressure (in $atm$)?

MediumKCET 2023

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$A$ vacuum vessel of volume $1 \, dm^3$ is evacuated at a constant temperature of $-23 \, ^\circ C$ until the pressure drops to $7.6 \times 10^{-5} \, torr$. What is the number of molecules remaining in the vessel?

Similar Questions

Calculate the temperature of $2 \text{ moles}$ of gas occupying a volume of $5.0 \text{ L}$ at a pressure of $24.6 \text{ atm}$. (Given: $R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}$) (in $^\circ \text{C}$)

An open vessel at $27\,^{\circ}C$ is heated until $3/5$ of the air in it has been expelled. Assuming the pressure remains constant,what is the final temperature of the vessel in $^{\circ}C$?

At a temperature of $27\,^oC$,a $2.461 \, L$ vessel contains $0.3 \, mol$ of $N_2$,$0.5 \, mol$ of $He$,and $6.2 \, mol$ of $O_2$ gases. What is the partial pressure of $N_2$ in $atm$?

If $4 \ g$ of $O_2$ and $2 \ g$ of $H_2$ are filled in a $1 \ L$ bulb at $0 \ ^oC$,the total pressure of the mixture will be...... (in $atm$)

$A$ gas at a pressure of $2 \ atm$ is heated from $25^{\circ} C$ to $323^{\circ} C$ and simultaneously compressed to $\frac{2}{3}$ of its original volume. What is the final pressure (in $atm$)?

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