Hello, Mimi;
I'm not sure what gas laws you've covered so far. Your book should have Charles; Law., .
Charles' Law- gives the relationship between volume and temperature if the pressure and the amount of gas are held constant:
This seems to fit your first problem well. The pressure and amount of gas are both constant between the two states.
V1/T1 = V2/T2
where 1 and 2 represent initial and final states. It is critical that temperatures be Kelvin in the gas law equations.
1) A sample of gas occupies 6.74 L at 325oC, what will its volume be at 25.0oC if the pressure does not change?
Set up a table with V1, T1, and T2, making sure you convert C to K by adding 273 the the Celsius value.
Since we want to find V2, let's rearrange the gas law:
V2 = V1(T2/T1)
Before we do math, let's eyeball what the answer should look like. We are reducing the temperature, with no change i n pressure. What happens to a e helium balloon if it gets cold? It shrinks. So we expect V2 will be smaller than V1. By how much? After we converted to Kelvin, the drop doesn't seem as dramatic as it was when using Celsius. But it drops by around a factor of two, so Let's watch to see if our answer is a smaller volume by around a factor of two;
Plug the numbers from the table into the equation above:
I see 3.36 L is the final volume. Did it shrink? YES. Did it shrink by around 1/2? YES. I'm haapy and ready to move on.
2) A balloon is inflated at room temperature of 22.0oC and has a volume of 3.86 L. The balloon is then heated to 51.0oC, what is the final volume?
This is solved with the same procedure as above. We can assume the pressure is constant, since we are only told that the balloon is inflated, but we will assume on Earth, and that it does not diksplace an appreciable amount of Earth's atmosphere. So the pressure will be the same, P1 = P2, or 1 atm.
Rearrange the same equation, make a table of the known values, and predict what will happen. We're heating the balloon, so I would expect it to respond. Once you've converted C to K, you can also guesstimate by how much. I didn't do the calculation, but am estimating the balloon should expand to by around 10%. So I would expect a new volume of around 3.3 L. Please let me know what you find.
3) A gas with a volume of 350.0 mL at 130.0oC is heated until the volume is 650.0 mL. What is the new temperature?
There is no mention of pressure change, so we can use the same law as above. Just rearrange the equation to find T2, the final temperature.
T2 = T1(V2/V1)
Make a table of the known values and convert C to K.
Again, without doing the math, we can see that V2/V1 nearly doubles. That would suggest that the temperature most also be around 2X the original. Even if they did not explicitly say that the balloon is heated, we know the temperature must rise for the balloon to expand by that amount, in the absence of a pressure change.
4) Exactly 4.00 L of air at -40.0oC is warmed to 100oC. What is the new volume if the pressure remains constant?
This is the same type of problem. Pressure constant and we want to find the new volume if the air is heated. Heating the air means it should expand, so V2 should be > V1. The increase in temperature, in Kelvin, from 233K to 373K, is an increase of around 50%. So I'm expecting the volume to be around a 50% increase, perhaps to 6 L.
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I hope this helps. Take it slowly and make clearly labelled tables - that process greatly reduces many math errors, and allows you to guestimate more easily. (guesstimate - Is that a real word?).
Bo b
