A gas in a closed container has a pressure of 6.40 atm at a temperature of 230 K. If the pressure in the container is decreased to 5.30 atm, what is the new temperature? a 890 K b 278 K c 83 K d 190 K
To solve this problem, we can use the combined gas law, which states: P1V1/T1 = P2V2/T2, where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
Given:
P1 = 6.40 atm
T1 = 230 K
P2 = 5.30 atm
Let's assume the volume remains constant, so V1 = V2. We can rewrite the equation as:
P1/T1 = P2/T2
Substituting the given values, we have:
6.40 atm / 230 K = 5.30 atm / T2
Simplifying the equation, we get:
6.40T2 = 5.30 * 230
T2 = (5.30 * 230) / 6.40
Calculating the right side of the equation, we have:
T2 = 191.0625 ≈ 191 K
Therefore, the new temperature is approximately 191 K, which is closest to 190 K (option d).
To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas. The formula for the combined gas law is:
(P₁ × V₁) / T₁ = (P₂ × V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures of the gas, respectively.
V₁ and V₂ are the initial and final volumes of the gas, respectively.
T₁ and T₂ are the initial and final temperatures of the gas, respectively.
In this problem, we are given:
P₁ = 6.40 atm
P₂ = 5.30 atm
T₁ = 230 K
T₂ = ?
Now we can plug in the given values into the combined gas law:
(6.40 atm × V₁) / 230 K = (5.30 atm × V₂) / T₂
The volume of the gas does not change in this problem, so we can drop the V₁ and V₂ terms:
6.40 / 230 = 5.30 / T₂
To find T₂, we can cross-multiply and solve for T₂:
5.30 × 230 = 6.40 × T₂
T₂ = (5.30 × 230) / 6.40
T₂ ≈ 190 K
Therefore, the new temperature is approximately 190 K. So, the correct answer is d) 190 K.
To solve this problem, we can use Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature (assuming volume remains constant).
First, let's write down the equation for Gay-Lussac's Law:
P1/T1 = P2/T2
Where:
P1 = initial pressure
T1 = initial temperature
P2 = final pressure
T2 = final temperature
Now let's plug in the given values into the equation:
P1 = 6.40 atm,
T1 = 230 K,
P2 = 5.30 atm,
T2 = unknown (let's call it x).
6.40/230 = 5.30/x
Cross multiplying, we get:
6.40x = 230 * 5.30
Now, divide both sides of the equation by 6.40 to solve for x:
x = (230 * 5.30) / 6.40
Calculating this expression, we find:
x ≈ 190 K
Therefore, the new temperature in the closed container, when the pressure is decreased to 5.30 atm, is approximately 190 K.
So the correct answer is d) 190 K.