Question

calculate root mean square of hydrogen at 800k

Answer 1

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

Answer:

$V_{rms}=1.845X10^3$

Explanation:

Mass of 1 mole of Hydrogen gas $=2 gm=2X10^{-3} kg$

$R = 8.314 Jmol^{-1}K^{-1}$

$T = 800K$

The formula of Vrms is $V_{rms} = \sqrt{\frac{3RT}{M}}$

⇒$V_{rms} = \sqrt{\frac{3RT}{M}}$

$= \sqrt{\frac{3X8.314Jmol^{-1}K^{-1}X800K}{2X10^{-3} }}$

Now, solving for Vrms we get:

$V_{rms}=\sqrt{3406.454X10^3}$

$V_{rms}=\sqrt{3.406X10^6}$

Taking the square root, we get:

$V_{rms}=1.845X10^3$

Hence, the root means the square velocity of hydrogen molecules at STP $1.845X10^3$.