Question

When a sample of a gas was placed in a sealed container with a volume of 3.45 L and heated to 105°C, the gas vaporized and the resulting pressure inside the container was 175.0 kPa. How many moles of the gas was present? Name the law that is used to solve this problem. Show your work.

Answer 1

approximately 0.0189 moles of the gas were present in the sealed container

Step-by-step explanation:

First, we need to convert the given values to the appropriate units. The volume is given as 3.45 L, so we convert it to cubic meters by dividing by 1000:

V = 3.45 L / 1000 = 0.00345 m³

The temperature is given as 105°C, so we need to convert it to Kelvin by adding 273.15:

T = 105°C + 273.15 = 378.15 K

The pressure is given as 175.0 kPa, so we need to convert it to Pascals by multiplying by 1000:

P = 175.0 kPa × 1000 = 175000 Pa

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

n = PV / RT

Substituting the given values:

n = (175000 Pa) × (0.00345 m³) / ((8.314 J/(mol·K)) × (378.15 K))

Calculating this expression:

n ≈ 0.0189 moles

Therefore, approximately 0.0189 moles of the gas were present in the sealed container.

The law used to solve this problem is the ideal gas law.