00:01
So for part a of this question, we're asked to calculate the empirical formula of the gas.
00:05
So we have the percent composition of each of the three elements within the compound.
00:11
So when we determine the empirical formula, we are going to assume we have a 100 gram sample just to make our calculations a little bit easier.
00:24
So if 24 .3 % of this 100 gram sample is carbon, that means we have 24 .3 grams of carbon.
00:35
Same with hydrogen, 4 .1 % of 100 gram sample, it's going to be 4 .1 grams.
00:41
And then the same for chlorine, 71 .7 % of 100 gram sample is 71 .7 grams of chlorine.
00:50
Now we can convert the grams into moles by taking each one times its molar mass.
00:59
Once we have the units into moles, we can compare those moles to determine the molar ratio of each of the elements in the compound, which will give us our empirical formula.
01:11
So first let's go with carbon.
01:12
We'll take it times its molar mass.
01:14
We want moles on top, grams on bottom.
01:17
Molar mass of carbon is 12 grams per mole.
01:20
So 24 .3 divided by 12, it's about 2 .025 moles of carbon.
01:30
Next we go to hydrogen.
01:33
Its molar mass is 1 .008 grams per mole.
01:38
We want moles on top, so that way the grams cancel out, right? grams on top cancel out with grams on bottom.
01:45
4 .1 divided by 1 .008 is 4 .07 moles of hydrogen.
01:53
Same with chlorine, we take it times its molar mass.
01:56
For every one mole of chlorine, we have 35 .45 grams of chlorine.
02:01
One gram is on bottom, so it cancels out with grams on top.
02:04
71 .7 divided by 35 .45 is going to be 2 .02 moles of chlorine.
02:15
Now to find the empirical formula, we take all of these moles divided by the smallest number, the smallest amount of moles.
02:28
So smallest amount of moles, right, is 2 .02.
02:30
That's the smallest one, so we are going to divide each of these by 2 .02, and that's going to give us a nice whole number that's going to tell us the empirical formula.
02:40
So we're going to take carbon divided by the 0 .202, which is going to be 1.
02:47
We're going to take 4 .07 divided by the 2 .02, which gives us 2.
02:53
And then 2 .02 divided by 2 .02 is going to be 1.
02:57
So our empirical formula is going to be 1 carbon, 2 hydrogens, 1 chlorine.
03:06
This is our empirical formula.
03:12
Next we're asked to determine how many moles of the gas are present.
03:17
So for this problem, we are going to use the ideal gas equation where pressure times volume is equal to the moles times r, the gas constant, times t, the temperature.
03:27
We're trying to calculate the moles, so we can rearrange that equation to get n by itself.
03:34
So n is going to be equal to pressure times volume divided by r times temperature.
03:39
So now we just have to plug in our values, which they give us in the equation.
03:44
But first we have to make sure all of these values are in the proper units.
03:50
We know r, our gas constant, is 0 .08201 liters times atmospheres over kelvin times moles...