Answer to Question #95757 in General Chemistry for Hassan Fallous

Question #95757
A cylinder contains 91.9 g of neon (Ne) gas. Another cylinder (twice the volume of the neon cylinder and at the same temperature/pressure), contains hydrogen (H2) gas.

Assuming both are ideal gases, what is the mass of the hydrogen gas (in g)?
1
Expert's answer
2019-10-03T05:19:07-0400

Let's use indeal gas law for the first cylinder


"pV = \\frac{{{m_{{\\text{Ne}}}}}}{{{M_{{\\text{Ne}}}}}}RT"


where "{{m_{{\\text{Ne}}}}}" - mass of Ne, "{{M_{{\\text{Ne}}}}}" - molar mass of Ne. We know, that pressure and temperature are the same in the second cylinder and "{V_2} = 2V" , so ideal gas law for the second cylinder will be


"2pV = \\frac{{{m_{{{\\text{H}}_2}}}}}{{{M_{{{\\text{H}}_2}}}}}RT"

Thus we can multiply the first equation by 2 and equalize the right sides


"\\frac{{{m_{{{\\text{H}}_2}}}}}{{{M_{{{\\text{H}}_2}}}}}RT = 2\\frac{{{m_{{\\text{Ne}}}}}}{{{M_{{\\text{Ne}}}}}}RT"

and express mass of the hydrogen


"{m_{{{\\text{H}}_2}}} = 2\\frac{{{M_{{{\\text{H}}_2}}}}}{{{M_{{\\text{Ne}}}}}}{m_{{\\text{Ne}}}}"

Now let's do the calculations (atomic weights can be found in the periodic table so "{M_{{\\text{Ne}}}} \\approx 20.18[\\frac{{\\text{g}}}{{{\\text{mol}}}}]" and "{M_{{{\\text{H}}_2}}} = 2 \\cdot {M_{\\text{H}}} \\approx 2 \\cdot 1.008[\\frac{{\\text{g}}}{{{\\text{mol}}}}] = 2.016[\\frac{{\\text{g}}}{{{\\text{mol}}}}]" )


"{m_{{{\\text{H}}_2}}} = 2\\frac{{2.016[\\frac{{\\text{g}}}{{{\\text{mol}}}}]}}{{20.18[\\frac{{\\text{g}}}{{{\\text{mol}}}}]}} \\cdot 91.9[{\\text{g}}] \\approx 18.36[{\\text{g}}]"






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