Question

What volume of carbon dioxide, at 1 atm pressure and 112°C, will be produced when 80.0 grams of methane is burned?

Answer 1

158 L.

Step-by-step 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:

`PV=nRT.`

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:

`80.0g\text{ CH}_4\cdot\frac{1\text{ mol CH}_4}{16\text{ g CH}_4}=5\text{ moles CH}_4.`

So, in this case, n=5.

Now, let's solve for 'V' and replace the given values in the ideal gas law equation:

`V=(nRT)/(P)=\frac{5\text{ moles }\cdot0.0821(L\cdot atm)/(mol\cdot K)\cdot385K}{1\text{ atm}}=158.04\text{ L}\approx158\text{ L.}`

The volume would be 158 L.