Question

calculate the root mean sqaure of hydrogen molecule at 800k?​

Answer 1

Answer:

Hey mate, here is your answer :

Square each value, add up the squares (which are all positive) and divide by the number of samples to find the average square or mean square. Then take the square root of that. This is the 'root mean square' (rms) average value.

Step: 1 OverviewFrom the equation of Kinetic Energy from Kinetic Molecular Theory, We know that:

K.E=(3/2)kT

(1/2)mvrms2=(3/2)kT

mvrms2=3kT

vrms2=(3kT)/m

Where k is constant has the value of 1.38x10-23Jmol-1K-1

Step: 2 CalculationGiven:

T=800K

k=1.38x10-23Jmol-1K-1

molecular mass of hydrogen molecule = 2 a.m.u = 2x1.67x10-27Kg = 3.34x10-27Kg

Solution:

According to above equation:

vrms2=(3kT)/m

vrms2=(3x1.38x10-23x800)/(3.34x10-27)

vrms2=(3.312x10-20)/(3.34x10-27)

vrms2=9.916x106

Taking square root both sides:

vrms=3148.96m/s2 (Ans).

Hope this answer helps you..

Answer 2

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

T = 800K.

Mass of Hydrogen = ${2 \times 10^{-3} \: Kg}$

(Taking in Kg as unit as it is S.I unit)

${\bold{R = gas constant = 8.3143 \: J \: mol^{-1} \: K^{-1}}}$

$\huge{\bold{\underline{Explanation:-}}}$

Root Mean Square Velocity.

It is the square root of the mean of the squares of the velocities of the molecules of gas.

Mathematically,

$\large{\bold{ v_{rms} = \sqrt{ \frac{ {v_1}^{2} + {v_2}^{2} + {v_3}^{2} + .......... + {v_{n}}^{2}}{n}}}}$

But, From Kinetic gas equation.

$\large{\bold{v_{rms} = \sqrt{ \frac{3RT}{M}} = \sqrt{ \frac{3PV}{M}} = \sqrt{ \frac{3P}{d}}}}$

Where

P = Pressure.

R = Gas constant.

V = Volume.

T = Temperature.

M = Molecular weight in Kg.

d = Density of the gas.

Considering.

$\large{\bold{ v_{rms} = \sqrt{ \frac{3RT}{M}}}}$

Substituting the values.

$\large{ v_{rms} = \sqrt{ \frac{ 3 \times 8.31 \times 800}{2 \times 10^{-3}}}}$

$\large{ v_{rms} = \sqrt{ \frac{ 19,944 \times 10^3}{2}}}$

Simplifying.

$\large{v_{rms} = \sqrt{ 9972 \times 10^3}}$

$\huge{\boxed{\boxed{v_{rms} = 3157.84 \: m/s}}}$

So,the root Mean square velocity of hydrogen molecule is 3,157.84 m/s.