Question

A vessel with an internal volume of 5.00 L contains 2.80 g of nitrogen gas, 0.403 g of hydrogen gas, and 79.9 g of helium gas. At 25°C, what is the pressure (in atm) inside the vessel?

Answer 1

The pressure inside the vessel can be calculated using the ideal gas law, which states that:

PV = nRT

where P is the pressure, V is the volume of the vessel, n is the number of moles of gas present, R is the gas constant, and T is the temperature in Kelvin.

Since we know the volume of the vessel (5.00 L) and the temperature (25°C), we can calculate the number of moles of gas present using the ideal gas law.

First, we need to convert the volume from liters to moles:

V = nRT / P

Now, we can substitute the values we know:

V = (2.80 g N2 + 0.403 g H2 + 79.9 g He) / (22.4 L-mol/mol-K x 25°C)

where 22.4 L-mol/mol-K is the molar volume of ideal gas at STP conditions (22.4 L/mol-K at 25°C and 1 atm).

Now, we can calculate the number of moles of each gas present:

N2 = (2.80 g N2) / (28.013 g/mol) = 0.100 mol

H2 = (0.403 g H2) / (2.016 g/mol) = 0.200 mol

He = (79.9 g He) / (4.004 g/mol) = 19.98 mol

Now, we can calculate the total number of moles of gas present:

n = N2 + H2 + He

= 0.100 mol + 0.200 mol + 19.98 mol

= 20.28 mol

Now, we can calculate the pressure inside the vessel using the ideal gas law:

P = nRT / V

= (20.28 mol) x (8.314 J/mol-K) x (25°C) / (5.00 L)

= 1013.25 atm

Therefore, the pressure inside the vessel is approximately 1013.25 atm.

Step-by-step explanation: