Question

Two 1 L flasks at T(K) contain O₂ and helium with rms velocities of x m s^-1 and y m s^-1, respectively. What is the relationship between x and y?

• A. 8 y$^2$ = x$^2$
• B. y$^2$ = 8 x$^2$
• C. y = x
• D. y = 8 x

Hint:

The square of the rms velocity is inversely proportional to the molar mass: $v_{{rms}}^2 \propto \frac{1}{M}$. Compare the ratio of molar masses to find the relationship.

Answer 1

The Correct Option is B

The rms velocity of a gas is given by \(v_{\text{rms}} = \sqrt{\frac{3RT}{M}}\), where \(M\) is the molar mass.
For O₂ (molar mass = 32 g mol^-1): \(x = \sqrt{\frac{3RT}{32}}\).
For He (molar mass = 4 g mol^-1): \(y = \sqrt{\frac{3RT}{4}}\).
Squaring both: \(x^2 = \frac{3RT}{32}\), \(y^2 = \frac{3RT}{4}\).
Taking the ratio: \(\frac{y^2}{x^2} = \frac{\frac{3RT}{4}}{\frac{3RT}{32}} = \frac{32}{4} = 8\).
Thus, \(y^2 = 8 x^2\).