Ideal gas calculation

Question

Consider a sample of helium in a 5.0 liter tank with a pressure of 785 mm Hg at a temperature of 18 degree Celsius.

What is the pressure of the gas in the atmosphere? pascals, kPa?

Answer 1

To convert the pressure of the helium gas from mm Hg to Pascal or kPa, we can use the following conversion factors:

1 mm Hg = 133.32 Pa 1 kPa = 1000 Pa

First, let's convert the temperature from Celsius to Kelvin:

T = 18 + 273.15 = 291.15 K

Next, we can use the ideal gas law to calculate the number of moles of helium in the tank:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.

Rearranging this equation to solve for n, we get:

n = PV/RT

n = (785 mm Hg) x (1 atm/760 mm Hg) x (5.0 L) / [(8.314 J/mol·K) x (291.15 K)]

n = 0.0088 mol

Now we can use the ideal gas law again to calculate the pressure of the gas in the atmosphere:

PV = nRT

P = nRT/V

P = (0.0088 mol) x (8.314 J/mol·K) x (291.15 K) / (5.0 L)

P = 127855 Pa

To convert to kPa, we divide by 1000:

P = 127.855 kPa

Therefore, the pressure of the helium gas in the atmosphere is approximately 127.855 kPa or 127855 Pa.