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 448 mm Hg and the temperature is 6.0°C?

I set it up like p1v1/t1= p2v2/t2 and got 940ml but it was wrong

To solve this problem, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure in atm
V = volume in liters
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin

Let's convert the given quantities to the appropriate units:

Initial conditions in the bag of potato chips:
V1 = 585 mL = 0.585 L
P1 = 765 mm Hg = 765/760 atm (since 1 atm = 760 mm Hg)
T1 = 25°C = 25 + 273.15 K

Conditions at the mountain top:
P2 = 448 mm Hg = 448/760 atm
T2 = 6.0°C = 6.0 + 273.15 K

Now we can rearrange the ideal gas law equation to solve for V2:

(V1/T1) * (P2/P1) = V2/T2

Substituting the given values:
(0.585/298.15) * (448/765) = V2/279.15

Now, let's calculate V2:

V2 = (0.585/298.15) * (448/765) * 279.15

V2 ≈ 0.301 L

Therefore, the volume of the potato chip bag at the top of the mountain would be approximately 0.301 liters.

To solve this problem, we can use the ideal gas law equation, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

In this case, we are assuming the bag of potato chips contains only air, so we can assume the number of moles of gas remains constant.

Let's break down the given information:

- The initial pressure, P1, is 765 mm Hg
- The initial volume, V1, is 585 mL
- The initial temperature, T1, is 25°C, which in Kelvin is 25 + 273 = 298 K

- The final pressure, P2, is 448 mm Hg
- The final temperature, T2, is 6.0°C, which in Kelvin is 6.0 + 273 = 279 K

We need to find the final volume, V2. Rearranging the ideal gas law equation gives us:

V2 = (P1 x V1 x T2) / (P2 x T1)

Plugging in the values:

V2 = (765 mm Hg x 585 mL x 279 K) / (448 mm Hg x 298 K)

First, let's convert the pressure values to the same units (mm Hg or atm), for example:

765 mm Hg = 765 / 760 = 1.006 atm
448 mm Hg = 448 / 760 = 0.589 atm

Now, we can calculate V2:

V2 = (1.006 atm x 585 mL x 279 K) / (0.589 atm x 298 K)
V2 = 1,637,205 / 175.222
V2 ≈ 9,319 mL

Therefore, the volume of the bag of potato chips at the top of the mountain would be approximately 9,319 mL.