Question

The speed of a longitudinal wave in a mixture of helium and neon at $300$ k was found to be $758$ m/s. The composition of the mixture would then be:

• A. $25.4$
• B. $4.3$
• C. $2.1$
• D. $4.1$

Answer 1

Answer: (B)

$4.3$

When $M_1=0.004kg/mol$) is mixed with $n_2$ moles of ($M_2=0.020kg/mol$), the equivalent molar mass of mix would be:

$M^{\prime }=\frac{n_1{M}_1+n_2{M}_2}{n_1+n_2}=\frac{4n_1+20n_2}{1000(n_1+n_2)}$

Both $He$ and $Ne$ are monoatomic so for mixture $\gamma =\frac{5}{3}$

so, the velocity of sound

$V=\sqrt{\frac{rRT}{M^{\prime }}}\Rightarrow M^{\prime }=\frac{\gamma RT}{V^2}(atT=300K)$

$\Rightarrow \frac{4n_1+20n_2}{1000(n_1+n_2)}=\frac{5\times 8.31\times 300}{3\times {\left(758\right)}^2}\simeq \frac{7}{1000}\Rightarrow \frac{n_1}{n_2}\simeq 4.33=\frac{13}{3}$