A gas occupies a volume of 140 mL at 35 degrees celcius and 97 kPa. What is the volume of the gas at STP? Please show the work.
(P1V1)/T1 = (P2V2)/T2
Don't forget to change T to Kelvin.
To find the volume of the gas at STP (Standard Temperature and Pressure), we need to use the ideal gas law equation: PV = nRT. Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L.atm/mol.K), and T is the temperature in Kelvin.
First, we need to convert 35 degrees Celsius to Kelvin.
T(K) = T(C) + 273.15
T(K) = 35 + 273.15
T(K) = 308.15 K
Now, we can plug the given values into the ideal gas law equation:
P₁V₁ = nRT
Since we are solving for the volume at STP, the pressure at STP is 1 atmosphere (atm), and we'll denote it as P₂ = 1 atm.
For the first set of conditions, we have:
P₁ = 97 kPa
V₁ = 140 mL = 0.14 L
T₁ = 308.15 K
R = 0.0821 L·atm/mol·K
Since the gas is the same, we can assume n and R are constant. The equation becomes:
P₁V₁ / T₁ = P₂V₂ / T₂
Now let's rearrange the equation to solve for V₂:
V₂ = (P₁V₁ × T₂) / (P₂ × T₁)
At STP, the temperature is 273.15 K and the pressure is 1 atm. Plugging these values into the equation, we get:
V₂ = (97 kPa × 0.14 L × 273.15 K) / (1 atm × 308.15 K)
To get the volume in the correct units, we need to convert the pressure from kilopascals (kPa) to atmospheres (atm). There are 101.325 kPa in 1 atm.
V₂ = (97 kPa × 0.14 L × 273.15 K) / (101.325 kPa × 308.15 K)
Now we can calculate V₂:
V₂ ≈ 0.038 L
Therefore, the volume of the gas at STP is approximately 0.038 L.