Hello, Mar,
The Ideal Gas Law states:
PV = nRT, where
P is the pressure, V is the volume, n is the moles of gas, R is the gas constant, and T is the temperature in Kelvin. All of these questions deal with the same moles of gas, so we can use a useful simplification of the gas law:
This equation states that we can find how changes from the initial conditions (subscript 1) will impact the final conditions (subscript 2), as long as the moles of gas do not change.
The next useful step is to set up a table with all the variables and their units, so that we can keep everything organized. There isn't room here for me to insert the table I made, but if you have a spreadsheet program such as Excel, you can both make a table and do the calculations right in the same program.
Imagine a table such as:
| P1 | 0.500 | atm | ||
| V1 | ||||
| T1 | 25 | C | 297 | K |
| P2 | ? | |||
| V2 | ||||
| T2 | 125 | C | 398 | K |
This is the data from the first question. We note that the volume does not change (no data given) so the change must occur in the same, rigid, container.
Put a "?" mark for the value you are looking for. Then let's rearrange the equation to find P2.
Since the volumes V1 = V2, they cancel out, leaving (P1/T1) = (P2/T2).
Rearrange to find P2, the unknown:
P2 = P1(T2/T1)
Make sure temperatures are in degrees Kelvin (add 273 to degrees C).
Now enter the data: P2 = (0.500atm)*(398 ⁰K/279 ⁰K)
P2 = 0.67 atm (2 sig figs since temperature (25) has two)
Do the same for the remainder of the problems. If pressures are in mmHg, then the same unit will appear in the final pressure, as in question 2. (I get 208 mmHg).
The third problem mixes ⁰C and ⁰K in the same question, but we can quickly spot the ruse when we have the data neatly presented in a table, and make the one temperature change to ⁰K.
It is very useful in all questions to imagine what is happening and then to predict what the outcome should look like. We you take a closed cylinder of gas and heat it, will the pressure go up or down? And if the temperature goes up by a factor of 2, will the pressure double? Predicting both the direction and approximate magnitude will help you spot big errors and correct them before moving on.
The last question tricks us into thinking the temperature is dropping (297 to 40), so we'd expect a pressure drop. But once we'd changed to 40⁰C to ⁰K, we see that the temperature is actually increasing, so the pressure should rise a little (297⁰K to 313⁰K, around a 5% increase.) I calculate a final pressure of 1.41 atm, which is up about 5%, so I'm content with the answer.
Bob
