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?

1 Answer
Aug 15, 2017

Answer:

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"#