Ammonia can decompose into nitrogen and hydrogen gas according to the equation below. Two NH3 reacts to form N2 plus three H2. 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?
In order to solve this problem, let’s first identify the given information. We know that when 17 grams of ammonia decomposes, three grams of hydrogen gas are produced. 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. 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. The name of this ratio is the molar ratio.
One way to solve this problem is to consider that the ratio of ammonia to hydrogen will always stay the same. 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. Remember that a proportion is when two ratios are equivalent to each other. 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.
Now, we can solve the proportion using cross multiplication. We know that 𝑥 must have the units grams. But for now, let’s solve for 𝑥 without using the units that are in the proportion. First, we get the equation 17𝑥 equals 34 times three. After simplifying, we get 17𝑥 equals 102. After dividing both sides of our equation by 17, we get 𝑥 equals six grams of hydrogen gas produced. If you’re going to use this method to solve problems, it’s important to make sure the proportion is set up correctly. 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. The unit present in the denominator must also be the same. In this case, it’s the mass of hydrogen in grams.
There is another way to solve this problem and calculate the same answer. Let’s review the steps in this method now. First, we’ll convert the amount in grams of ammonia to moles. Next, we’ll convert the amount in moles of ammonia to the amount in moles of hydrogen. Finally, we’ll convert the amount in moles of hydrogen to grams.
Now, let’s complete the calculation using conversion factors. 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. During this step, the units grams of ammonia are canceled. In step two, we’ll need to use the molar ratio to convert from moles of ammonia to moles of hydrogen. We need to remember that when writing the molar ratio, we need to use the coefficients from the balanced chemical equation.
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. We need to make sure to place two moles of ammonia in the denominator to cancel out the units of moles of ammonia.
Now, we’re ready to move on to step three. 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. In this step, the units moles of hydrogen are canceled.
Now that we’ve set up all three conversion factors, we’re ready to calculate the amount in grams of hydrogen gas produced. First, we’ll divide 34 by 17, then multiply by three, divide by two, and finally multiply by two. In conclusion, the amount of hydrogen gas produced by the decomposition of 34 grams of ammonia is six grams.