A beam of hydrogen molecules H2 is directed toward a wall, atn angle of 55o the
ID: 1743212 • Letter: A
Question
A beam of hydrogen molecules H2 is directed toward a wall, atn angle of 55o the normal to the wall. Each molecule in the beam has a speedof 1.0 km/s and a mass of 3.3 x 10^-24 g. The beam strikes the wallover an area of 2.0 cm^2, at the rate of 10^23 molecules persecond. What is the beam's pressure on the wall?
Formulas of concern: nM(vrms^2) / 3V where M represents the molar mass of Hydrogen which is givenin my textbook as 2.02 x 10^-3 kg/mol
also the textbook give Vrms = 1920 m/s for hydrogen molecule @room temperature
n (number of moles in a sample) = Msample/M
I calculated n
n= 3.3x10^-27 kg / 2.02 x 10 ^-3 kg/mol n=1.634 x 10 ^-24 mol
Then i got extremely stuck as I am unsure how to getVolume..Could anyone help me please?
I know and (Vavg)^2=3p/ where represents density, p representspressure
Explanation / Answer
Given : A = 2.0 cm2 = 2.0 x 10-4m2 m = 3.3 x10-27 kg,N / t = 1023moles/s,
v = 1.0 x 103m/s
The change in momentum is p = Ft
(2Nmvcos) = Ft F = 2(N/t)mvcos Pressure = F/A
=(2(N/t)mvcos)/A = (2 * 1023 moles/s * 3.3 x 10-27 kg *1.0 x103 m/s * cos55o)/(2.0 x 10-4m2) =1.89 kPa
I hope it helps you m = 3.3 x10-27 kg,
N / t = 1023moles/s,
v = 1.0 x 103m/s
The change in momentum is p = Ft
(2Nmvcos) = Ft F = 2(N/t)mvcos F = 2(N/t)mvcos Pressure = F/A
=(2(N/t)mvcos)/A = (2 * 1023 moles/s * 3.3 x 10-27 kg *1.0 x103 m/s * cos55o)/(2.0 x 10-4m2) =1.89 kPa
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