A bag of potato chips contains 575mL of air at 25.0∘C and a pressure of 765mmHg .
Assuming the bag does not break, what will be its volume at the top of a mountain where the pressure is 458mmHg and the temperature is 10.0∘C?
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (765 mmHg)
V1 = initial volume (575 mL)
T1 = initial temperature (25.0 °C)
P2 = final pressure (458 mmHg)
V2 = final volume (unknown)
T2 = final temperature (10.0 °C)
Let's plug in the given values:
(765 mmHg * 575 mL) / (25.0 °C) = (458 mmHg * V2) / (10.0 °C)
Now, let's solve for V2:
(765 mmHg * 575 mL * 10.0 °C) = (458 mmHg * V2 * 25.0 °C)
To isolate V2, divide both sides of the equation by (458 mmHg * 25.0 °C):
V2 = (765 mmHg * 575 mL * 10.0 °C) / (458 mmHg * 25.0 °C)
V2 ≈ 502.89 mL
Therefore, the volume of the bag of potato chips at the top of the mountain would be approximately 502.89 mL.
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (765 mmHg)
V1 = initial volume (575 mL)
T1 = initial temperature (25.0 °C + 273.15 = 298.15 K)
P2 = final pressure (458 mmHg)
V2 = final volume (to be found)
T2 = final temperature (10.0 °C + 273.15 = 283.15 K)
Substituting the values into the equation, we get:
(765 mmHg * 575 mL) / (298.15 K) = (458 mmHg * V2) / (283.15 K)
Now, we can solve for V2 by rearranging the equation:
V2 = [(765 mmHg * 575 mL) / (298.15 K)] * (283.15 K / 458 mmHg)
Calculating this expression, we find:
V2 ≈ 796 mL
Therefore, the volume of the bag at the top of the mountain would be approximately 796 mL.