Answer:
158 L.
Explanation:
What is given?
Pressure (P) = 1 atm.
Temperature (T) = 112 °C + 273 = 385 K.
Mass of methane CH4 (g) = 80.0 g.
Molar mass of methane CH4 = 16 g/mol.
R constant = 0.0821 L*atm/mol*K.
What do we need? Volume (V).
Step-by-step solution:
To solve this problem, we have to use ideal gas law: the ideal gas law is a single equation which relates the pressure, volume, temperature, and number of moles of an ideal gas. The formula is:
[tex]PV=nRT.[/tex]Where P is pressure, V is volume, n is the number of moles, R is the constant and T is temperature.
So, let's find the number of moles that are in 80.0 g of methane using its molar mass. This conversion is:
[tex]80.0g\text{ CH}_4\cdot\frac{1\text{ mol CH}_4}{16\text{ g CH}_4}=5\text{ moles CH}_4.[/tex]So, in this case, n=5.
Now, let's solve for 'V' and replace the given values in the ideal gas law equation:
[tex]V=\frac{nRT}{P}=\frac{5\text{ moles }\cdot0.0821\frac{L\cdot atm}{mol\cdot K}\cdot385K}{1\text{ atm}}=158.04\text{ L}\approx158\text{ L.}[/tex]The volume would be 158 L.
