Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • In a container filled with a gas, the molecules have a root mean square speed <img alt="\left(V_{\text {rms }}\right)" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%28V_%7B%5Ctext%20

In a container filled with a gas, the molecules have a root mean square speed \left(V_{\text {rms }}\right) of 222 \mathrm{~m} / \mathrm{s}. The total number of gas molecules in the container is 2.22 \times$ $10^{23}. Calculate the average pressure exerted by these gas molecules on the container walls. The molecular mass of the gas is 3 \mathrm{~g} / \mathrm{mol}, and the volume of the container is 3 liters.

Option: 1

8.133 \times 10^{5} Pascal


Option: 2

81.33 \times 10^{5} Pascal


Option: 3

8.133 \times 10^{4} Pascal


Option: 4

8133 \times 10^{5} Pascal


Answers (1)

best_answer

Let's start by identifying the given values:

\begin{aligned} & V_{\mathrm{rms}}=222 \mathrm{~m} / \mathrm{s} \\ & N=2.22 \times 10^{23} \text { molecules } \\ & m=3 \mathrm{~g} / \mathrm{mol} \quad \text { (molecular mass of the gas) } \\ & V=3 \text { liters } \quad \text { (volume of the container) } \end{aligned}

The average force F from N molecules can be written as:

F=\frac{m \cdot N \cdot V_{\mathrm{rms}}^{2}}{3 \cdot V}

The pressure P in the container is expressed as:

P=\frac{2 \cdot N \cdot m \cdot V_{\mathrm{rms}}^{2}}{3 \cdot V^{2}}

Let's convert the molecular mass from grams to kilograms (1 \mathrm{~g}=0.001 \mathrm{~kg}) and the volume from liters to cubic meters ( 1 liter =0.001 cubic meters):

\begin{aligned} & m=3 \mathrm{~g} / \mathrm{mol} \cdot(0.001 \mathrm{~kg} / \mathrm{g})=0.003 \mathrm{~kg} / \mathrm{mol} \\ & V=3 \text { liters } \cdot(0.001 \text { cubic meters } / \text { liter })=0.003 \text { cubic meters } \end{aligned}

Calculate the average force F :

F=\frac{0.003 \mathrm{~kg} / \mathrm{mol} \cdot 2.22 \times 10^{23} \text { molecules } \cdot(222 \mathrm{~m} / \mathrm{s})^{2}}{3 \cdot 0.003 \text { cubic meters }}

Calculate the pressure P in the container:

P=\frac{2 \cdot 0.003 \mathrm{~kg} / \mathrm{mol} \cdot 2.22 \times 10^{23} \text { molecules } \cdot(222 \mathrm{~m} / \mathrm{s})^{2}}{3 \cdot(0.003 \text { cubic meters })^{2}}

Solve for pressure P :

P=\frac{2 \cdot 0.003 \mathrm{~kg} / \mathrm{mol} \cdot 2.22 \times 10^{23} \text { molecules } \cdot(222 \mathrm{~m} / \mathrm{s})^{2}}{3 \cdot(0.003 \text { cubic meters })^{2}} \approx 8.133 \times 10^{5} \mathrm{~Pa}

The pressure is in Pascal. If you wish to convert it to a different unit (e.g., atm, \mathrm{mmHg}, etc.), use the appropriate conversion factor.

So, the average pressure exerted by the gas molecules on the container walls is approximately 8.133 \times 10^{5} Pascal.

 

Posted by

Gaurav

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

Karnataka NEET UG Counselling 2025: KEA opens applications for MBBS, BDS admissions
anam-khan

Karnataka NEET UG merit list 2025 out; 87,909 to take part in MBBS, BDS, AYUSH counselling
anam-khan

‘Will affect lakhs of candidates’: Supreme Court, HC refuse NEET UG 2025 re-exam, result revision pleas

Latest Question