Answer to Question #97062 in General Chemistry for Brittany Wallace

Question #97062
1. A sample of methane gas collected at a pressure of 226 mm Hg and a temperature of 286 K has a mass of 20.1 grams. The volume of the sample is __L.
2. A 24.3 gram sample of krypton gas has a volume of 927 milliliters at a pressure of 3.71 atm. The temperature of the Kr gas sample is ___°C.
1
Expert's answer
2019-10-22T05:43:43-0400

Problem 1.

Methane has chemical formula "C{H_4}" and molar mass "{M_{C{H_4}}} \\approx 16.043[{{\\rm{g}} \\over {{\\rm{mol}}}}]" . To solve the problem we can use ideal gas law

"pV = \\nu RT"

where "R \\approx 8.314[{{\\rm{J}} \\over {{\\rm{K}} \\cdot {\\rm{mol}}}}]" - universal gas constant and "\\nu = {m \\over {{M_{C{H_4}}}}}" - the amount of moles of methane.

Thus, the volume


"V = {1 \\over p}{m \\over {{M_{C{H_4}}}}}RT"

Let's do the calculations, using that "1[{\\rm{mmHg}}] \\approx 133.322[{\\rm{Pa}}]"


"V = {1 \\over {226 \\cdot 133.322[{\\rm{Pa}}]}}{{20.1[{\\rm{g}}]} \\over {16.043[{{\\rm{g}} \\over {{\\rm{mol}}}}]}}8.314[{{\\rm{J}} \\over {{\\rm{K}} \\cdot {\\rm{mol}}}}] \\cdot 286[{\\rm{K}}] \\approx 0.0989[{{\\rm{m}}^3}] \\approx 98.87[{\\rm{L}}]"

Problem 2.

Krypton "Kr" has a molar mass "{M_{Kr}} \\approx 83.798[{{\\rm{g}} \\over {{\\rm{mol}}}}]". Using the same ideal gas law we get for the temperature


"T = {{pV} \\over {\\nu R}} = {{{M_{Kr}}} \\over m}{{pV} \\over R}"

Let's do the calculations, using that "1[{\\rm{atm}}] = 101325[{\\rm{Pa}}]"


"T = {{83.798[{{\\rm{g}} \\over {{\\rm{mol}}}}]} \\over {24.3[{\\rm{g}}]}}{{3.71 \\cdot 101325[{\\rm{Pa}}] \\cdot 927 \\cdot {{10}^{ - 6}}[{{\\rm{m}}^{\\rm{3}}}]} \\over {8.314[{{\\rm{J}} \\over {{\\rm{K}} \\cdot {\\rm{mol}}}}]}} \\approx 144.54[{\\rm{K}}] \\approx - 128.61[{\\rm{^\\circ C}}]"


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