A gas is collected and found to fill 2.85L at 25.0 degrees Celsius. What will be its volume at standard temperature?
(P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
To learn
To find the volume of the gas at standard temperature, we can use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure of the gas (atmospheres)
- V is the volume of the gas (liters)
- n is the number of moles of the gas
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature of the gas (Kelvin)
The standard temperature is defined as 0 degrees Celsius or 273.15 Kelvin.
We need to convert the initial temperature from Celsius to Kelvin:
25.0 degrees Celsius + 273.15 = 298.15 Kelvin
Now we can rearrange the ideal gas law equation to solve for the volume at standard temperature:
V₁ / T₁ = V₂ / T₂
Where:
- V₁ is the initial volume of the gas
- V₂ is the volume of the gas at standard temperature
- T₁ is the initial temperature of the gas
- T₂ is the temperature at standard temperature
Let's substitute the given values into the equation:
V₁ = 2.85 L
T₁ = 298.15 K (initial temperature)
T₂ = 273.15 K (standard temperature)
V₂ / 273.15 K = 2.85 L / 298.15 K
Now we can solve for V₂ by cross multiplying:
V₂ = (2.85 L * 273.15 K) / 298.15 K
V₂ ≈ 2.62 L
Therefore, the volume of the gas at standard temperature is approximately 2.62 liters.
To find the volume of a gas at standard temperature, we need to use the Combined Gas Law equation, which is a variation of the Ideal Gas Law. The Combined Gas Law is written as:
(P₁ × V₁) / (T₁) = (P₂ × V₂) / (T₂)
In this equation:
- P₁ and P₂ are the initial and final pressures
- V₁ and V₂ are the initial and final volumes
- T₁ and T₂ are the initial and final temperatures, measured in Kelvin (℃ + 273.15)
In this case, we are given the initial volume (V₁ = 2.85 L) and temperature (T₁ = 25.0 ℃). We want to find the final volume (V₂) at standard temperature, which is 0 ℃ or 273.15 K.
Step 1: Convert the initial temperature from Celsius to Kelvin:
T₁ = 25.0 ℃ + 273.15 = 298.15 K
Step 2: Substitute the known values into the Combined Gas Law equation:
(P₁ × V₁) / (T₁) = (P₂ × V₂) / (T₂)
We know that P₂ is equal to the pressure at standard temperature, which is usually given as 1 atm.
Step 3: Solve for V₂:
V₂ = (P₁ × V₁ × T₂) / (P₂ × T₁)
Substituting the known values:
V₂ = (1 atm × 2.85 L × 273.15 K) / (1 atm × 298.15 K)
Calculating the equation:
V₂ ≈ 2.62 L
Therefore, the volume of the gas at standard temperature (0 ℃ or 273.15 K) would be approximately 2.62 L.