Question

What is the molecular mass of a gas if 3.7 g of the gas at 25 °C occupy the same volume as 0.184 g of hydrogen at 17 °C and the same pressure?

Answer 1

The molecular mass of the gas is 42 u.

Explanation:

We can use the Ideal Gas Law to solve this problem:.

`color(blue)(bar(ul(|color(white)(a/a)pV = nRTcolor(white)(a/a)|)))" "`

Since `n = m/M`, we can rearrange this equation to get

`pV = (m/M)RT`

And we can solve this equation to get

`M = (mRT)/(pV)`

In this problem, we have two gases.

We can write

`M_1 = (m_1RT_1)/(pV)` and `M_2 = (m_2RT_2)/(pV)`

Dividing `M_2` by `M_1`, we get

`M_2/M_1 = (m_2color(red)(cancel(color(black)(R)))T_2)/(color(red)(cancel(color(black)(pV)))) × (color(red)(cancel(color(black)(pV))))/(m_1color(red)(cancel(color(black)(R)))T_1) = (m_2T_2)/(m_1T_1)`

`M_2 = M_1 × m_2/m_1 × T_2/T_1`

In this problem,

`M_1 = "2.016 u";color(white)(mmmmmmmmml) M_2 = ?`
`m_1 = "0.184 g";color(white)(mmmmmmmmmll) m_2 = "3.7 g"`
`T_1 = "(17 + 273.15) K" = "290.15 K"; T_2 = "(25 + 273.15) K" = "298.15 K"`

∴ `M_2 = "2.016 u" × (3.7 color(red)(cancel(color(black)("g"))))/(0.184 color(red)(cancel(color(black)("g")))) × (298.15 color(red)(cancel(color(black)("K"))))/(290.15 color(red)(cancel(color(black)("K")))) = "42 u"`