What is the volume of 325 mL of a sample of gas at 51.0°C and 710. mm Hg if the conditions are adjusted to STP? Assume the amount of gas is held constant.
(P1V1/T1) = (P2V2/T2)
Don't forget T is in Kelvin.
To find the volume of the gas at STP, we can use the combined gas law equation, which relates the initial conditions of the gas to the conditions at STP.
The combined gas law equation is as follows:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure (in mm Hg)
V₁ = initial volume (in mL)
T₁ = initial temperature (in Kelvin)
P₂ = final pressure at STP (which is 760 mm Hg)
V₂ = final volume at STP (what we are solving for)
T₂ = final temperature at STP (which is 273.15 K)
Let's solve for V₂:
Convert the initial temperature from Celsius to Kelvin:
T₁ = 51.0°C + 273.15 = 324.15 K
Now, substitute the given values into the combined gas law equation:
(710 mm Hg * 325 mL) / (324.15 K) = (760 mm Hg * V₂) / (273.15 K)
To solve for V₂, rearrange the equation:
V₂ = (710 mm Hg * 325 mL * 273.15 K) / (760 mm Hg * 324.15 K)
V₂ = (710 * 325 * 273.15) / (760 * 324.15)
V₂ ≈ 263 mL
Therefore, the volume of the gas at STP is approximately 263 mL.
To calculate the volume of gas at STP (Standard Temperature and Pressure), we need to understand the relationship between temperature, pressure, and volume using the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant
T = temperature
At STP, the conditions are defined as 0°C (273.15 K) and 1 atmosphere (760 mm Hg).
Step 1: Convert the given temperature to Kelvin.
To convert Celsius to Kelvin, add 273.15.
51.0°C + 273.15 = 324.15 K
Step 2: Convert the pressure from mm Hg to atm.
Since the pressure is given in mm Hg, we need to convert it to atm by dividing by 760 (because 1 atm = 760 mm Hg).
710. mm Hg / 760 mm Hg/atm = 0.93421 atm
Step 3: Calculate the volume at STP.
We are given the volume as 325 mL. However, we need to convert it to liters (L) because the ideal gas constant (R) is expressed in liters per mole.
325 mL / 1000 mL/L = 0.325 L
Step 4: Determine the moles of gas.
Since the amount of gas is held constant, the moles of gas are also constant at both conditions.
We can rearrange the Ideal Gas Law equation to solve for moles (n):
n = PV / RT
Substituting the values we know:
n = (0.93421 atm) * (0.325 L) / [(0.0821 L·atm/mol·K) * (324.15 K)]
Solving this equation will give us the moles of gas.
Step 5: Calculate the volume at STP.
Now we can rearrange the Ideal Gas Law equation to solve for the volume at STP (V₂):
V₂ = (n * R * T₂) / P₂
Substituting the values we know:
n = [calculated in Step 4]
R = 0.0821 L·atm/mol·K
T₂ = 273.15 K
P₂ = 1 atm
Solving this equation will give us the volume of gas at STP.