A 6.0-cm-diameter cylinder of Nitrogen gas has a 4.0-cm-thick movable copper pis

Question

A 6.0-cm-diameter cylinder of Nitrogen gas has a 4.0-cm-thick movable copper piston. The cylinder is oriented vertically, and the air above the piston is evacuated. When the gas temperature is 20 degrees Celsius, the piston floats 20cm above the bottom of the cylinder. a. What is the gas pressure? b. How many gas molecules are in the cylinder?
A 6.0-cm-diameter cylinder of Nitrogen gas has a 4.0-cm-thick movable copper piston. The cylinder is oriented vertically, and the air above the piston is evacuated. When the gas temperature is 20 degrees Celsius, the piston floats 20cm above the bottom of the cylinder. a. What is the gas pressure? b. How many gas molecules are in the cylinder?

Explanation / Answer

Hi, We know mass = density * volume

Hence Mass of piston = ? * V = ? * p * r^2 * h Pressure = F/A = Mg/A = ? * p * r^2 * h * g / p * r^2 = ? * h * g

  g = 9.80 m/sec^2
  We know density of copper = 8.96 g/cm^3.     i.e., ? = 8.96 g/cm^3 = 8.96 * 10^3 kg/m^3
Hence Pressure = 8960 * 0.04 * 9.8 = 3512 N/m^2 = 3512 Pa. = 3.512 kpa b) We know PV = nRT   (where R is universal Gas Constant)       Given temperature = 20 deg celcius = 293 deg kelvin.       height of cylinder column = 20 cm = 0.2 m       radius of cylinder = 6cm / 2 = 3cm       Volume of the cylinder = p * r^2 * height = 3.14 * 0.03^2 * 0.2                                         = 0.0005652 m^3         Hence the numbr of moles of nitrogen gas = n = PV / RT                                         = 3512 * 0.0005652 / 8.314472 * 293
                                        = 8.14 * 10(-4)                                         = 8.14 * 10(-4)     We know each mole of a gas contains avagadro number of molecules.
    Hence the number of nitrogen molecules in the cylinder                                        = 8.14 * 10(-4) * 6.023*10^23                                        = 49.027 * 10^(19) molecules.                                        = 49.027 * 10^(19) molecules. Hope this help you.

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