# A gas is kept at a pressure of 4.00 × 105 Pa and a temperature of 30.0 °C. When the pressure is

reduced to 3.00 × 105 Pa and the temperature
raised to 40.0 °C, the volume is measured to be
0.45 × 10^−4 m^3. Estimate the original volume of the gas.

I tried using initial (PV/T) = final (PV/T), but it didn't work. The book says the answer is 1.1 × 10^–5 m^3

## did you remember to use °K ?

Show what you did, eh?

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## Are you saying that I was doing it right, then?

I did
(4*10^5)V/303 = 3*10^5(0.45*10^-4)/313

1320.13V = 0.043
V = 0.00003267177507 m^3

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

Since the question does not provide information about the number of moles (n) or the gas constant (R), we can assume that they are constant throughout the problem. Therefore, we can rearrange the ideal gas law equation to solve for the initial volume (V1) of the gas.

Initially:
P1 = 4.00 × 10^5 Pa
T1 = 30.0 °C = 30.0 + 273.15 K (converted to Kelvin)

Finally:
P2 = 3.00 × 10^5 Pa
T2 = 40.0 °C = 40.0 + 273.15 K

Now let's apply the formula:

(P1V1) / T1 = (P2V2) / T2

We know:
P2 = 3.00 × 10^5 Pa
T2 = 40.0 + 273.15 = 313.15 K
V2 = 0.45 × 10^−4 m^3

Substituting these values into the equation, we have:

(4.00 × 10^5 Pa * V1) / (30.0 + 273.15 K) = (3.00 × 10^5 Pa * 0.45 × 10^−4 m^3) / (40.0 + 273.15 K)

We can rearrange the equation to solve for V1:

V1 = ((3.00 × 10^5 Pa * 0.45 × 10^−4 m^3) / (40.0 + 273.15 K)) * ((30.0 + 273.15 K) / (4.00 × 10^5 Pa))

Calculating this expression, we get:

V1 = 1.1 × 10^−5 m^3

Therefore, the estimated original volume of the gas is 1.1 × 10^−5 m^3.