WEBVTT
00:00:03.290 --> 00:00:09.590
Ammonia can decompose into nitrogen and hydrogen gas according to the equation below.
00:00:10.050 --> 00:00:15.470
Two NH3 reacts to form N2 plus three H2.
00:00:15.750 --> 00:00:27.900
If 17 grams of ammonia produces three grams of hydrogen gas, then how much hydrogen gas is produced by the decomposition of 34 grams of ammonia?
00:00:28.480 --> 00:00:33.350
In order to solve this problem, let’s first identify the given information.
00:00:33.630 --> 00:00:40.520
We know that when 17 grams of ammonia decomposes, three grams of hydrogen gas are produced.
00:00:40.960 --> 00:00:51.940
But we need to determine how much hydrogen gas is produced, which we will label as 𝑥, when the decomposition reaction begins with 34 grams of ammonia.
00:00:52.290 --> 00:01:01.860
We know that in a balanced chemical equation, the ratio between the amount of moles of any two substances in the equation is a fixed ratio.
00:01:02.210 --> 00:01:05.210
The name of this ratio is the molar ratio.
00:01:05.420 --> 00:01:12.860
One way to solve this problem is to consider that the ratio of ammonia to hydrogen will always stay the same.
00:01:13.090 --> 00:01:22.630
Therefore, we can create a proportion to solve the problem by comparing the mass of the reactant, ammonia, to the mass of the product, hydrogen.
00:01:22.840 --> 00:01:27.920
Remember that a proportion is when two ratios are equivalent to each other.
00:01:28.170 --> 00:01:40.740
Therefore, if 17 grams of ammonia yields three grams of hydrogen in the reaction, we can set this equal to 34 grams of ammonia yields 𝑥 amount of hydrogen gas.
00:01:41.090 --> 00:01:44.770
Now, we can solve the proportion using cross multiplication.
00:01:44.980 --> 00:01:47.950
We know that 𝑥 must have the units grams.
00:01:48.060 --> 00:01:52.940
But for now, let’s solve for 𝑥 without using the units that are in the proportion.
00:01:53.240 --> 00:01:57.890
First, we get the equation 17𝑥 equals 34 times three.
00:01:58.080 --> 00:02:02.240
After simplifying, we get 17𝑥 equals 102.
00:02:02.450 --> 00:02:10.150
After dividing both sides of our equation by 17, we get 𝑥 equals six grams of hydrogen gas produced.
00:02:10.490 --> 00:02:16.350
If you’re going to use this method to solve problems, it’s important to make sure the proportion is set up correctly.
00:02:16.550 --> 00:02:25.680
You need to ensure that the same unit is in the numerator in both parts of the proportion, which in our case is the amount of ammonia in grams.
00:02:25.880 --> 00:02:29.270
The unit present in the denominator must also be the same.
00:02:29.410 --> 00:02:32.620
In this case, it’s the mass of hydrogen in grams.
00:02:32.890 --> 00:02:36.780
There is another way to solve this problem and calculate the same answer.
00:02:37.030 --> 00:02:39.570
Let’s review the steps in this method now.
00:02:39.660 --> 00:02:43.680
First, we’ll convert the amount in grams of ammonia to moles.
00:02:44.040 --> 00:02:49.650
Next, we’ll convert the amount in moles of ammonia to the amount in moles of hydrogen.
00:02:49.990 --> 00:02:54.110
Finally, we’ll convert the amount in moles of hydrogen to grams.
00:02:54.460 --> 00:02:58.460
Now, let’s complete the calculation using conversion factors.
00:02:58.690 --> 00:03:08.930
Let’s begin by converting 34 grams of ammonia to moles by dividing by the molar mass of ammonia, which is 17 grams per one mole.
00:03:09.220 --> 00:03:13.050
During this step, the units grams of ammonia are canceled.
00:03:13.350 --> 00:03:20.450
In step two, we’ll need to use the molar ratio to convert from moles of ammonia to moles of hydrogen.
00:03:20.670 --> 00:03:27.950
We need to remember that when writing the molar ratio, we need to use the coefficients from the balanced chemical equation.
00:03:28.150 --> 00:03:37.960
When looking at the coefficients in the balanced chemical equation, for every two moles of ammonia that react, three moles of hydrogen gas are produced.
00:03:38.300 --> 00:03:46.030
We need to make sure to place two moles of ammonia in the denominator to cancel out the units of moles of ammonia.
00:03:46.310 --> 00:03:48.470
Now, we’re ready to move on to step three.
00:03:48.730 --> 00:03:59.550
To convert from moles of hydrogen to grams of hydrogen, we need to multiply by the molar mass of diatomic hydrogen or H2, which is two grams per one mole.
00:03:59.610 --> 00:04:03.200
In this step, the units moles of hydrogen are canceled.
00:04:03.570 --> 00:04:10.830
Now that we’ve set up all three conversion factors, we’re ready to calculate the amount in grams of hydrogen gas produced.
00:04:11.030 --> 00:04:19.660
First, we’ll divide 34 by 17, then multiply by three, divide by two, and finally multiply by two.
00:04:19.860 --> 00:04:28.300
In conclusion, the amount of hydrogen gas produced by the decomposition of 34 grams of ammonia is six grams.