What is the number of oxygen molecules in a c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The ideal gas equation is given by $PV = NkT$,where $P$ is pressure,$V$ is volume,$N$ is the number of molecules,$k$ is the Boltzmann constant,and

Vedclass · Accepted Answer

$3.3 	imes 10^{21}$

Vedclass · Answer

(C) The ideal gas equation is given by $PV = NkT$,where $P$ is pressure,$V$ is volume,$N$ is the number of molecules,$k$ is the Boltzmann constant,and $T$ is the temperature in Kelvin.Given: $P = 13.8 \ Pa$,$V = 1 \ m^3$,$k = 1.38 	imes 10^{-23} \ JK^{-1}$,and $T = 27^{\circ}C = 27 + 273 = 300 \ K$.Rearranging the formula for $N$: $N = \frac{PV}{kT}$.Substituting the values: $N = \frac{13.8 	imes 1}{1.38 	imes 10^{-23} 	imes 300}$.$N = \frac{13.8}{414 	imes 10^{-23}} = \frac{13.8}{4.14 	imes 10^{-21}} = \frac{13.8}{414} 	imes 10^{23} = 0.0333 	imes 10^{23} = 3.33 	imes 10^{21}$.Thus,the number of molecules is approximately $3.3 	imes 10^{21}$.

What is the number of oxygen molecules in a cylinder of volume $1 \ m^3$ at $27^{\circ}C$ and $13.8 \ Pa$? (Boltzmann constant $k = 1.38 \times 10^{-23} \ JK^{-1}$)

Similar Questions

During an experiment, an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expands to a volume $2V$?

Hydrogen gas is filled in a balloon at $20^\circ C$. If the temperature is increased to $40^\circ C$ while the pressure remains constant,what fraction of the original Hydrogen gas will escape from the balloon?

The volume of a gas at $21^{\circ}C$ temperature and $768 \,mm$ pressure is $1 \,L$. If the density of the gas is $1.2 \,g/L$ at $NTP$,then its mass will be ..... $g$.

Equal molar amounts of $H_2$ and $He$ are placed in two separate containers of equal volume at the same temperature. Their molar masses are $2$ and $4$ respectively. If the pressure of $H_2$ gas is $4 \ atm$,what will be the pressure of $He$ gas in atmospheres?

$A$ hydrogen cylinder is designed to withstand an internal pressure of $100 \,atm$. At $27^{\circ} C$,hydrogen is pumped into the cylinder which exerts a pressure of $20 \,atm$. At what temperature does the danger of explosion first set in? (in $K$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module