7.7mol of helium are in a 16L cylinder. The pressure gauge on the cylinder reads 65psi. What are (a) the temperature of the gas in Celsius and (b) the average kinetic energy of a helium atom?
Part A:
so this is what i did
T=PV/nR and C=T-273
P=65psi=4.481592e^5Pa
V=16L=.016m^3
n=7.7mole
R=8.31
so T=.1663155895
C=-272.8336844
this is incorrect
I'm waiting for part a to work on part b
I will assume that the 65 psi is the absolute pressure (psia), although most pressure gauges that read that high would be reading gauge pressure. 65 psia is 4.42 atm
PV/nT = R = 0.08205 atm-liter/(mole*K)
T = PV/(nR) = 4.42*16/(7.7*.08205) = 112 K
The average kinetic energy per atom is (3/2)kT. The molecular weight does not matter. k is Boltzmann's constant, 1.38*10^-23 J/K
I appreciate your help but this isn't working out
To determine the temperature of the gas in Celsius (part a), you correctly used the ideal gas law equation:
T = PV/nR
However, there seems to be a mistake in the conversion of pressure from psi to Pascals. The conversion factor is 1 psi = 6.895 × 10^3 Pa, not 4.481592 × 10^5 Pa. Let's fix that.
Given:
P = 65 psi × (6.895 × 10^3 Pa/1 psi) = 4.47475 × 10^5 Pa
V = 16 L = 0.016 m^3
n = 7.7 mol
R = 8.31 J/(mol·K)
Plug in the values:
T = (4.47475 × 10^5 Pa) × (0.016 m^3) / (7.7 mol) × (8.31 J/(mol·K))
Now, calculate T:
T = 130.160237 K
To convert from Kelvin to Celsius, subtract 273.15:
T = 130.160237 K - 273.15 = -142.989763 °C
Therefore, the temperature of the gas in Celsius is approximately -143 °C.
Now let's move onto part b to determine the average kinetic energy of a helium atom.
The average kinetic energy (KE) of a gas is given by the equation:
KE = (3/2) * (k * T)
Where:
k is the Boltzmann constant (1.380649 × 10^-23 J/K)
T is the temperature in Kelvin (130.160237 K)
Plug in the values:
KE = (3/2) * (1.380649 × 10^-23 J/K) * (130.160237 K)
Now calculate KE:
KE = 3.207434 × 10^-22 J
Therefore, the average kinetic energy of a helium atom is approximately 3.21 × 10^-22 J.