A syringe containing 1.59 mL of oxygen gas is cooled from 90.0 °C to 0.7 °C. What is the final volume V of oxygen gas? (Assume that the pressure is constant.)
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (constant)
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, we need to convert the initial and final temperatures to Kelvin:
Initial temperature = 90.0 °C = 90.0 + 273.15 = 363.15 K
Final temperature = 0.7 °C = 0.7 + 273.15 = 273.85 K
Since the pressure is constant, we can simplify the equation to:
V1/T1 = V2/T2
Where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
Substitute the given values:
1.59 mL / 363.15 K = V / 273.85 K
Solve for V:
V = (1.59 mL * 273.85 K) / 363.15 K
V = 1.19 mL
Therefore, the final volume of the oxygen gas is 1.19 mL.