Question

The ratio of total kinetic energy of 1.87 gram of hydrogen and 5.53 gram of oxygen at 300 kelvin s

Answer 1

Answer: The ratio of the total kinetic energies of the given amount of hydrogen and oxygen will be 27 : 5

Explanation:

Hydrogen and oxygen are the diatomic gases and the formula for kinetic energy is given as:

$K.E.=\frac{5}{2}nRT$    ....(1)

where,

R = Gas constant

T = Temperature of the gas  

n = Number of moles of gas  

To calculate the number of moles, we use the formula:  

$n=\frac{\text{Given mass}}{\text{Molar mass}}$

For Hydrogen:  

Molar mass = 2g/mol  

Given mass = 1.87g  

$n_H=\frac{1.87}{2}=0.935mol$

For Oxygen:

Molar mass = 32g/mol

Given mass = 5.53g

$n_H=\frac{5.53}{32}=0.1728mol$

Taking the ratio of kinetic energy of hydrogen and oxygen by putting it in equation 1, we get:  

$\frac{E_H}{E_O}=\left ( \frac{0.935\times \frac{5}{2}RT}{0.1728\times \frac{5}{2}RT} \right )\\\\\frac{E_H}{E_O}=\frac{5.4}{1}$

For converting this into whole number, we multiply both numerator and denominator by 5, we get:

$\frac{E_H}{E_O}=\frac{5.4\times 5}{1\times 5}=\frac{27}{5}\\\\E_H:E_O=27:5$

Hence, the ratio of the total kinetic energies of the given amount of hydrogen and oxygen will be 27 : 5