A syringe containing 1.65mL of oxygen gas is cooled from 91.3∘C to 0.5∘C.
What is the final volume of oxygen gas?
I got 2.19ml???
Close. I punched in the numbers like this and obtained
1.65 mL x (364.45/273.65) = 2.1975 which I would round to 2.20 mL and not 2.19.
To find the final volume of oxygen gas, we can use the ideal gas law:
PV = nRT
Where:
P is the pressure of the gas (assumed constant)
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature (Ti) = 91.3 + 273.15 = 364.45 K
Final temperature (Tf) = 0.5 + 273.15 = 273.65 K
Since the syringe is sealed and the gas is not allowed to escape, the number of moles (n) stays constant.
So we have:
(Vi/Ti) = (Vf/Tf)
Now, let's solve for Vf (final volume). Rearranging the equation, we get:
Vf = (Vi * Tf) / Ti
Plugging in the values:
Vi = 1.65 mL
Tf = 273.65 K
Ti = 364.45 K
Vf = (1.65 * 273.65) / 364.45
Vf ≈ 1.24 mL
Therefore, the final volume of oxygen gas is approximately 1.24 mL, not 2.19 mL.
To calculate the final volume of the oxygen gas, we can make use of Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin. The equation that represents Charles's Law is:
V1 / T1 = V2 / T2
where:
V1 is the initial volume of the gas
T1 is the initial temperature of the gas in Kelvin
V2 is the final volume of the gas (what we want to find)
T2 is the final temperature of the gas in Kelvin
First, let's convert the temperatures from Celsius to Kelvin. The conversion from Celsius to Kelvin is given by the equation:
T(K) = T(°C) + 273.15
Initial temperature (T1) = 91.3°C + 273.15 = 364.45 K
Final temperature (T2) = 0.5°C + 273.15 = 273.65 K
Now, we can rearrange the equation and solve for V2:
V2 = (V1 * T2) / T1
Substituting the values:
V2 = (1.65 mL * 273.65 K) / 364.45 K
Calculating this:
V2 = 1.23 mL
Therefore, based on the calculations, the final volume of the oxygen gas should be approximately 1.23 mL, not 2.19 mL.