Final answer:
Using the combined gas law, the final moles of gas in the container after temperature and pressure changes is approximately 0.806 moles when rounded to three significant figures.
Step-by-step explanation:
Calculating Moles of Gas After Pressure and Temperature Changes
To find out how many moles of the gas sample are present at the end, the ideal gas law can be applied. However, as conditions change and part of the gas is released, we'll use the combined gas law which relates pressure, volume, and temperature, as the volume remains constant. The equation is:
P1/T1 = P2/T2 × (n2/n1)
Where P represents pressure, T represents temperature in Kelvin (K), n represents moles, and the subscripts 1 and 2 represent initial and final conditions, respectively.
Let's calculate the final amount of moles (n2):
- Convert the initial and final temperatures to Kelvin by adding 273.15:
- T1 = 21.7 °C + 273.15
- = 294.85 K
- T2 = 28.1 °C + 273.15
- = 301.25 K
- Plug in the known values into the equation and solve for n2:
- (3.75 atm / 294.85 K) = (0.998 atm / 301.25 K) × (n2/1.70 moles)
- Calculate n2:
- n2 = (0.998 atm / 301.25 K) × (294.85 K / 3.75 atm) × 1.70 moles
- n2 = 0.806 moles (rounded to three significant figures)
The final amount of moles of the gas present in the container at the end is approximately 0.806 moles.