Question

A container with a one-liter capacity at 27° C is filled with helium to a pressure of 2.0 atm. (1 atm = 1.0 × 105 N/m2.) How many moles of helium does it hold?

Answer 1

To determine the number of moles of helium in the container, we can use the ideal gas law equation:

PV = nRT

Where:

P = pressure (in atm)

V = volume (in liters)

n = number of moles

R = ideal gas constant (0.0821 L·atm/mol·K)

T = temperature (in Kelvin)

First, we need to convert the temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15

T(K) = 27°C + 273.15 = 300.15 K

Now we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

Plugging in the given values:

P = 2.0 atm

V = 1.0 L

R = 0.0821 L·atm/mol·K

T = 300.15 K

n = (2.0 atm * 1.0 L) / (0.0821 L·atm/mol·K * 300.15 K)

n ≈ 0.0802 moles

Therefore, the container holds approximately 0.0802 moles of helium.