Question

which of the following gases diffuse more slowly than oxygen?
c₂h₂
no
ne
n₂o
a gas of unknown identity diffuses at a rate of 80.4 ml/s in a diffusion apparatus in which carbon dioxide diffuses at the rate of 102 ml/s. calculate the molecular mass of the unknown gas.
g/mol
which of the following is the possible identity of the unknown gas from the previous question?
h₂
kr
cl₂
o₂

Explanation:

Step1: Calculate molar mass of gases in first question

• Molar mass of \(O_2\) is \(M_{O_2}=32\space g/mol\)
• Molar mass of \(C_2H_2\) is \(M_{C_2H_2}=(2\times12 + 2\times1)=26\space g/mol\)
• Molar mass of \(NO\) is \(M_{NO}=(14 + 16)=30\space g/mol\)
• Molar mass of \(Ne\) is \(M_{Ne}=20.18\space g/mol\)
• Molar mass of \(N_2O\) is \(M_{N_2O}=(2\times14+16)=44\space g/mol\)
• According to Graham's law of diffusion \(r\propto\frac{1}{\sqrt{M}}\), gas with higher molar mass diffuses slower. Since \(M_{N_2O}>M_{O_2}\), \(N_2O\) diffuses slower than \(O_2\)

Step2: Calculate molar mass of unknown gas

• Let \(r_1 = 80.4\space mL/s\) (rate of unknown gas), \(r_2=102\space mL/s\) (rate of \(CO_2\)), \(M_2 = 44\space g/mol\) (molar mass of \(CO_2\))
• By Graham's law \( \frac{r_1}{r_2}=\sqrt{\frac{M_2}{M_1}}\)
• \(M_1 = M_2\times(\frac{r_2}{r_1})^2\)
• \(M_1=44\times(\frac{102}{80.4})^2\)
• \(M_1 = 44\times(\frac{1020}{804})^2=44\times(\frac{170}{134})^2\)
• \(M_1 = 44\times\frac{28900}{17956}\approx70.9\space g/mol\)

Step3: Identify the gas

• Molar mass of \(H_2\) is \(M_{H_2} = 2\space g/mol\)
• Molar mass of \(Kr\) is \(M_{Kr}=83.8\space g/mol\)
• Molar mass of \(Cl_2\) is \(M_{Cl_2}=70.9\space g/mol\)
• Molar mass of \(O_2\) is \(M_{O_2} = 32\space g/mol\)

Answer:

First question: \(N_2O\)
Second question: \(70.9\space g/mol\)
Third question: \(Cl_2\)