Calculate the number of total atoms and molecules in $4 \, L$ of $SO_2$ gas at $350 \, K$ temperature and $10^3 \, Pa$ pressure. $[R = 8.3144 \, J \, K^{-1} \, mol^{-1}]$.
(N/A) Using the ideal gas equation $PV = nRT$:
$n = \frac{PV}{RT} = \frac{10^3 \, Pa \times 4 \times 10^{-3} \, m^3}{8.3144 \, J \, K^{-1} \, mol^{-1} \times 350 \, K} \approx 1.374 \times 10^{-4} \, mol$.
Number of molecules $= n \times N_A = 1.374 \times 10^{-4} \times 6.022 \times 10^{23} \approx 8.275 \times 10^{19} \, \text{molecules}$.
Since each $SO_2$ molecule has $3$ atoms,total atoms $= 3 \times 8.275 \times 10^{19} \approx 2.483 \times 10^{20} \, \text{atoms}$.
$n = \frac{PV}{RT} = \frac{10^3 \, Pa \times 4 \times 10^{-3} \, m^3}{8.3144 \, J \, K^{-1} \, mol^{-1} \times 350 \, K} \approx 1.374 \times 10^{-4} \, mol$.
Number of molecules $= n \times N_A = 1.374 \times 10^{-4} \times 6.022 \times 10^{23} \approx 8.275 \times 10^{19} \, \text{molecules}$.
Since each $SO_2$ molecule has $3$ atoms,total atoms $= 3 \times 8.275 \times 10^{19} \approx 2.483 \times 10^{20} \, \text{atoms}$.
Explore More
Similar Questions
At a constant temperature,two different gases $G_1$ and $G_2$ are kept in separate flasks. The molar mass of $G_2$ is three times that of $G_1$,while the density of $G_1$ is two times that of $G_2$. What is the ratio of the pressure exerted by $G_2$ to that of $G_1$ in their respective flasks?
Difficult
View SolutionIn terms of Charles' law,explain why $-273.15 \,^{\circ}C$ is the lowest possible temperature.
Medium
View SolutionAt what temperature in $K$ will $28 \ g$ of $N_2$ gas occupy a volume of $10.0 \ L$ at $2.46 \ atm$ pressure?
Medium
View SolutionIf $P, V,$ and $T$ represent the pressure,volume,and temperature of a gas,respectively,which of the following represents Boyle's Law correctly?
Easy
View Solution$A$ home owner uses $4.00 \times 10^{3} \ m^{3}$ of methane $(CH_{4})$ gas (assume $CH_{4}$ is an ideal gas) in a year to heat his home. Under the pressure of $1.0 \ atm$ and $300 \ K$,the mass of gas used is $X \times 10^{5} \ g$. The value of $X$ is $.......$ (Nearest integer).
(Given $R = 0.083 \ L \ atm \ K^{-1} \ mol^{-1}$)
(Given $R = 0.083 \ L \ atm \ K^{-1} \ mol^{-1}$)
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo