Gas Compression Problem: New Pressure Calculation
What is the new pressure of a gas after compressing it from 534 mL to 167 mL at a constant temperature and initial pressure of 894 torr?
Choose the correct answer:
- A. 3.762 atm
- B. 4.523 atm
- C. 2.315 atm
- D. 5.678 atm
Answer:
A. 3.762 atm
The new pressure of the gas can be calculated using the ideal gas law formula, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. At constant temperature and with no change in the number of moles, the equation can be simplified to (P₁V₁) = (P₂V₂).
Given that the initial pressure (P₁) is 894 torr and initial volume (V₁) is 534 mL, and the final volume (V₂) is 167 mL, we can apply the formula as follows:
∴ P₂ = (P₁V₁)/V₂ = (894.0 torr)(534.0 mL)/(167.0 mL) = 2859 torr.
Converting the pressure from torr to atm using the conversion factor 1.0 atm = 760.0 torr, we get:
P₂ = (2859 torr)(1.0 atm/760 torr) = 3.762 atm.
Therefore, the new pressure of the gas after compression is 3.762 atm.