A bag of potato chips contains 585 mL of air at 25°C and a pressure of 765 mm Hg. Assuming the bag does not break, what will be its volume at the top of a mountain where the pressure is 434 mm Hg and the temperature is 4.3°C?
(P1V1/T1) = (P2V2/T2)
Don't forget T is in Kelvin.
Hello sir/madam I'm going through coursera and I have a difficulty in solving a problem of chemistry. I holp you will help me out to solve this.
To solve this problem, we can use the combined gas law formula, which relates the initial and final conditions of pressure, volume, and temperature of a gas.
The combined gas law formula is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
Let's plug in the given values into the formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
(P1 * 585 mL) / (25°C + 273.15) = (434 mm Hg * V2) / (4.3°C + 273.15)
Converting the temperatures to Kelvin:
(P1 * 585 mL) / (298.15 K) = (434 mm Hg * V2) / (277.45 K)
Now let's solve for V2, the final volume:
V2 = (434 mm Hg * V2) / (277.45 K) * (585 mL) / (P1)
Substituting the given values:
V2 = (434 mm Hg * 585 mL) / (277.45 K * 765 mm Hg)
Calculating the final volume:
V2 = (252990 mm Hg * mL) / (212.32 K * mm Hg)
Simplifying:
V2 = 1193.81 mL
Therefore, the volume of the bag of potato chips at the top of the mountain, where the pressure is 434 mm Hg and the temperature is 4.3°C, will be approximately 1193.81 mL.
To find the volume of the bag of potato chips at the top of the mountain, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure (765 mm Hg)
V₁ = initial volume (585 mL)
T₁ = initial temperature (25°C)
P₂ = final pressure (434 mm Hg)
V₂ = final volume (unknown)
T₂ = final temperature (4.3°C)
First, let's convert the temperatures to Kelvin by adding 273.15 to each temperature:
T₁ = 25°C + 273.15 = 298.15 K
T₂ = 4.3°C + 273.15 = 277.45 K
Now we can substitute the values into the formula:
(765 mm Hg * 585 mL) / (298.15 K) = (434 mm Hg * V₂) / (277.45 K)
Next, solve the equation for V₂:
(765 mm Hg * 585 mL) * (277.45 K) = (434 mm Hg * V₂) * (298.15 K)
(765 * 585 * 277.45) / (434) = V₂
V₂ ≈ 987.88 mL
Therefore, the volume of the bag of potato chips at the top of the mountain, where the pressure is 434 mm Hg and the temperature is 4.3°C, would be approximately 987.88 mL.