Question

At 278 K, the speed of H₂ gas molecules will be ____ times faster than the speed of O₂ molecules and their ratio (urms(H₂)/urms(O₂) _____ when the temperature increases.

four, will not change

four, will increase

sixteen, will not change

sixteen, will decrease

Not enough information is given to answer this question.

Answer 1

The velocity of a gas in terms of R.M.S velocity is given by the formula Vrms =  

in this equation , R - is the universal gas constant (8.314JK-1mol-1 )

M- is the molecular mass

T - is the temperature

Now we want to compare the ratio of Vrms(H2) to Vrms(O2). Here R,T are constant and the only thing that is varying is the molecular mass of the gas.

The molecular mass of H2 = 2g/mol

The molecular mass of O2 = 32g/mol

So writing the equation of both these gas incorporating the molecular mass,

Vrms(H2) =

Vrms(O2) =

Now taking the ratio of both Vrms(O2) and Vrms(H2) all the constant terms that is R,T will be cancelled. So we will be taking the ratio of square root of molecular mass of both H2  and O2. So,

Vrms(H2) / Vrms(O2) =

So, Vrms(H2) = 4 * Vrms(H2) (ANS)

So speed of H2 is 4 times the speed of O2.

Since, from the equation , Vrms =   , we can see that Vrms

Since there is a direct proportionality between Vrms and with increase in temperature there is an increase in Vrms. But here in the question we are asked to check the change in ratio of Vrms(H2) / Vrms(O2) with increase in temperature. So at a particular temperature the temperature terms for the velocity of both H2 and  O2  will cancel each other. This means that there is no change in ratio of Vrms(H2) / Vrms(O2) with increase in temperature. So Vrms(H2) / Vrms(O2) will not change with increase in temperature.

Ans)- At 278 K, the speed of H2 gas molecules will be _4___ times faster than the speed of O2 molecules and their ratio (urms(H2)/urms(O2) __will not change___ when the temperature increases.