Final answer:
To calculate the density of ethane at 920 torr and 245 K, one must first convert the pressure to atm and then apply the Ideal Gas Law rearranged to solve for the density, which involves the molar mass of ethane and the gas constant in appropriate units.
Step-by-step explanation:
The density of ethane (C2H6) in a vessel at a given pressure and temperature can be calculated using the Ideal Gas Law, which is PV = nRT. In this formula, P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Converting the pressure from torr to atm (since 1 atm is 760 torr) and using the gas constant R in appropriate units, we can then rearrange the equation to solve for density (d = m/V = nM/V), where M is the molar mass of ethane.
Firstly, we start by converting the pressure from torr to atm:
Pressure (P) = 920 torr * (1 atm / 760 torr) = 1.2105 atm
Now, we can use the Ideal Gas Law rearranged to solve for m/V (density, d), where M is the molar mass of ethane (30.07 g/mol):
d = PM / RT
Using R = 0.0821 L·atm / K·mol and substituting the values we get:
d = (1.2105 atm) * (30.07 g/mol) / (0.0821 L·atm / K·mol) * (245 K)
By computing these values, we can find the density of ethane under the given conditions.