the volume of a gas measured at 27 c and 101.3 kpa is 20.0 dm3 what final temperature would be required to increase the volume too 40.0 at 101 kpa
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure in kPa
V1 = Initial volume in dm3
T1 = Initial temperature in Kelvin
P2 = Final pressure in kPa
V2 = Final volume in dm3
T2 = Final temperature in Kelvin
We are given:
P1 = 101.3 kPa
V1 = 20.0 dm3
T1 = 27°C (300 K)
P2 = 101 kPa
V2 = 40.0 dm3
Let's plug in the values and solve for T2:
(101.3 kPa * 20.0 dm3) / (300 K) = (101 kPa * 40.0 dm3) / T2
Now, we can solve for T2:
(101.3 kPa * 20.0 dm3 * T2) = (101 kPa * 40.0 dm3 * 300 K)
(2026 kPa * dm3 * T2) = (4040 kPa * dm3 * K)
T2 = (4040 kPa * dm3 * K) / (2026 kPa * dm3)
T2 ≈ 2 K
Therefore, the final temperature required to increase the volume to 40.0 dm3 at 101 kPa is approximately 2 K.
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of temperature, pressure, and volume of a gas.
The combined gas law is given as:
(P₁ × V₁) ÷ (T₁) = (P₂ × V₂) ÷ (T₂)
Where:
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
Let's assign the following values to the variables:
P₁ = 101.3 kPa (initial pressure)
V₁ = 20.0 dm³ (initial volume)
P₂ = 101.0 kPa (final pressure)
V₂ = 40.0 dm³ (final volume)
We want to find the final temperature, T₂. The initial temperature, T₁, is given as 27°C, which needs to be converted to Kelvin.
To convert Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
So, T₁ = 27°C + 273.15 = 300.15 K
Now, let's plug the values into the combined gas law equation and solve for T₂:
(P₁ × V₁) ÷ (T₁) = (P₂ × V₂) ÷ (T₂)
(101.3 kPa × 20.0 dm³) ÷ (300.15 K) = (101.0 kPa × 40.0 dm³) ÷ (T₂)
Simplifying the equation:
(101.3 × 20) ÷ (300.15) = (101.0 × 40) ÷ (T₂)
2026.0 ÷ 300.15 = 4040.0 ÷ T₂
T₂ = (4040.0 × 300.15) ÷ 2026.0
T₂ ≈ 599.2 K
Therefore, the final temperature required to increase the volume to 40.0 dm³ at 101.0 kPa would be approximately 599.2 K.