To determine the volume occupied by 0.5 moles of methane gas at Standard Temperature and Pressure (STP), we need to use the properties of gases at these conditions.
At STP, which is defined by a temperature of 273.15 K (0°C) and a pressure of 1 atm, one mole of an ideal gas occupies a volume of 22.4 liters, which is equivalent to 22,400 milliliters (mL).
Given:
- Number of moles of methane gas (n) = 0.5 moles
- Volume occupied by 1 mole of gas at STP = 22,400 mL
To find the volume occupied by 0.5 moles of methane gas, we can use the following proportional relationship:
[tex]\[ \text{Volume of gas} = \text{Number of moles} \times \text{Volume occupied by one mole} \][/tex]
Plugging in the values:
[tex]\[ \text{Volume of gas} = 0.5 \, \text{moles} \times 22,400 \, \text{mL/mole} \][/tex]
Perform the multiplication:
[tex]\[ \text{Volume of gas} = 11,200 \, \text{mL} \][/tex]
Therefore, 0.5 moles of methane gas at STP occupies a volume of 11,200 mL.
