Question

A bulb of capacity $1d{m}^3$ contains $1.03\times {10}^{23}{H}_2$ molecules & pressure exerted by these molecules is 101.325 kpa. Calculate the average square molecular speed and the temperature?

• A. $4.44\times {10}^5{\left(m/s\right)}^2;171.27K$
• B. $8.88\times {10}^5{\left(m/s\right)}^2;71.27K$
• C. $8.88\times {10}^7{\left(m/s\right)}^2;35.58K$
• D. $1.224{\left(m/s\right)}^2;71.27K$

Answer 1

Answer: (D)

$1.224{\left(m/s\right)}^2;71.27K$

Average square molecular speed $={\left(\frac{3PV}{M}\right)}^{0.5}$

$={\left(\frac{3\times \frac{101.325}{101.321}\times 1}{2}\right)}^{0.5}$

$=1.224m^2/s^2$

The temperature would be:

$T=\frac{PV}{nR}=\frac{1\times 1}{\frac{1.03\times {10}^{23}}{6.023\times {10}^{23}}\times 0.0821}=71.27K$

Hence, the correct option is $\text{D}$