Video Transcript
How much water can be produced from 4.800 grams of oxygen and 0.5846 grams of hydrogen? Give your answer to the nearest two decimal places. The molar mass of hydrogen is one gram per mole and oxygen is 16 grams per mole.
To begin, we may initially think about the law of conservation of mass, which states that in a closed system, the mass of reactants of a chemical reaction will equal the mass of the products. However, this assumes that all of the reactant molecules are completely consumed during the reaction. So if 4.800 grams of oxygen and 0.5846 grams of hydrogen are completely consumed during a reaction, then we’d expect that 5.3846 grams of water should be produced. In order to determine if the masses of both reactants are completely consumed, we need to rely on our knowledge of stoichiometry. We need to find out if a limiting reactant is present, which would limit the amount of the product, water, being formed.
In order to solve this problem and determine the mass of water formed in the reaction, we need to calculate the amount of water each reactant would produce if fully consumed. The reactant that could produce less water is the limiting reactant and therefore determines the amount of water produced. Because we are using stoichiometry to solve this problem, a balanced chemical equation is needed.
Let’s start by writing the chemical formulas of the reactants. The chemical formula for diatomic oxygen is O2, and the chemical formula for diatomic hydrogen is H2. The reactants are always written on the left side of the reaction arrow in a chemical equation. The products are written on the right side of the reaction arrow. And in this reaction, there is one product, water, which has the chemical formula H2O. We can begin by noticing that the reactant side of the equation has two oxygen atoms and the product side only has one oxygen atom. Therefore, we should add a coefficient of two in front of water on the product side.
Now that we’ve balanced the oxygen atoms, let’s take a look at the hydrogen atoms. On the reactant side of the equation, there are two hydrogen atoms, and on the product side, there are four hydrogen atoms. In order to balance the hydrogen atoms, we need to place a coefficient of two in front of hydrogen on the reactant side. Now that we have a balanced chemical equation, we can determine which reactant is the limiting reactant. Based on our calculations, the reactant that produces less water is the limiting reactant and therefore determines the amount of water produced.
In our calculations, we’ll need to perform the following three steps with each reactant. In the problem, 4.800 grams of oxygen is present. First, we need to convert from grams of oxygen to moles of oxygen. We do this by dividing by the molar mass of O2, which is 32 grams per one mole. This molar mass is calculated by taking the average molar mass of oxygen given in the problem and multiplying by two. Notice that in this first step, we have canceled the unit of grams of O2.
Now we’re ready to convert from moles of oxygen to moles of water. In this step, we’ll need to use the molar ratio of water to oxygen and make use of the coefficients in the balanced equation. According to the equation, for every one mole of oxygen that reacts, two moles of water are produced. We’ll need to write one mole of oxygen in the denominator, which allows us to cancel the units of moles of oxygen. Now we’re ready for step three. To convert from moles of water to grams of water, we need to multiply by the molar mass of water, which is 18 grams per one mole. This molar mass is calculated by adding together the average molar mass of two hydrogen atoms and one oxygen atom. Notice that in step three, the units of moles of water are canceled.
Now we can calculate the amount in grams of water produced. Let’s start with 4.800 and divide by 32. Then, we multiply by two and finally multiply by 18. Therefore, if all of the oxygen is consumed, 5.400 grams of water could be produced. While we may be tempted to accept this as the correct answer, we don’t know for sure because we have not calculated how much water can be produced from 0.5846 grams of hydrogen.
To do so, let’s repeat the three steps for hydrogen. To convert from grams of hydrogen to moles of hydrogen, we need to divide by the molar mass of H2, which is two grams per mole. This molar mass is calculated by taking the average molar mass of hydrogen provided in the problem and multiplying by two. Like before, during the step, we cancel the units of grams of H2. Now, we’re ready to convert from moles of H2 to moles of water. We’ll need to use the molar ratio. When looking at the balanced chemical equation, we see that for every two moles of hydrogen that react, two moles of water are produced.
When writing the mole ratio, we need to place two moles of hydrogen in the denominator. This allows us to cancel the units of moles of hydrogen. Finally, we can convert to grams of water by multiplying by water’s molar mass, which is 18 grams per mole. In this step, the units of moles of water are canceled. Now we’re ready to calculate the grams of water produced. Let’s start with 0.5846 grams and divide by two. Next, we’ll multiply by two, divide by two, and finally multiply by 18. Therefore, if all of the hydrogen is consumed during the reaction, 5.2614 grams of water could be produced. Since the mass of water produced from hydrogen is smaller, hydrogen is the limiting reactant.
Therefore, with the amounts of reactants given in the problem, only 5.2614 grams of water can be produced. After rounding to two decimal places, the correct answer is 5.26 grams.
