Answer to Question #97061 in General Chemistry for Brittany Wallace

Question #97061
1. A sample of nitrogen gas occupies a volume of 8.98 L at 51 °C and 0.4560 atm. If the volume of the gas sample is increased to 11100 mL, while its temperature is decreased to -1 °C, the resulting gas pressure, in torr, will be___ torr.

2. 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.
1
Expert's answer
2019-10-22T05:43:46-0400

Problem 1.

Let's 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" is the amount of moles. Using this law for the first and the second state we get


"{p_1}{V_1} = \\nu R{T_1}""{p_2}{V_2} = \\nu R{T_2}"

Divide the second by the first


"{{{p_2}{V_2}} \\over {{p_1}{V_1}}} = {{{T_2}} \\over {{T_1}}}"

and for the pressure at the second state


"{p_2} = {p_1}{{{V_1}} \\over {{V_2}}}{{{T_2}} \\over {{T_1}}}"

Let's do the calculations using that "T[K] = T[^\\circ C] + 273.15" and "1[{\\rm{atm}}] = 760[{\\rm{torr}}]"


"{p_2} = 0.456[{\\rm{atm}}]{{9.98[{\\rm{L}}]} \\over {11100 \\cdot {{10}^{ - 3}}[{\\rm{L}}]}}{{272.15[{\\rm{K}}]} \\over {324.15[{\\rm{K}}]}} \\approx 0.3442[{\\rm{atm}}] \\approx 261.592[{\\rm{torr}}]"

Problem 2.

Let's use the ideal gas law again


"pV = \\nu RT"

Methane has the chemical formula "C{H_4}" and has the molar mass "{M_{C{H_4}}} \\approx 16.043[{{\\rm{g}} \\over {{\\rm{mol}}}}]". The number of moles can be found as "\\nu = {m \\over M}" , thus


"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}}]"


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