First let's convert the 10.00 grams of H2O into moles of H2O. We do this by finding the molar mass of H2O. Remember that the molar mass is the number of grams of a substance in 1 mole of the substance. So the molar mass of H2O can be thought of as the number of grams of H2O in 1 mole of H2O.
So how do we find the molar mass of H2O? We begin by looking on the periodic table to find the atomic masses of H and O. H is the symbol for hydrogen, and its atomic mass is 1.008. Remember that the H in H2O has a subscript (the little number that is written right after the H). The subscript for H is 2. This means that we have 2 Hs in H2O. The atomic mass for one H is 1.008 but we have 2 Hs in H2O. So we have to do 2 x 1.008 in order to find the total grams of H in H2O. The calculator says that 2 x 1.008 = 2.016. So we know that there are 2.016 grams of H in the molar mass of H2O. Now we turn to the O in H2O. O is the symbol for oxygen, and its atomic mass is 15.999. The O in H2O has no subscript, so we know that there is only one O in H2O. Now we add the grams of H and the grams of O together. We have 2.016 grams of H and 15.999 grams of O. If we add them together, the calculator says that 2.016 + 15.999 = 18.015 grams. So we know the molar mass of H2O.
Molar mass of H2O = 18.015 grams of H2O in one mole of H2O.
Remember that we found the molar mass of H2O so that we could convert 10.00 grams of H2O into moles of H2O. We set up the equation to turn 10.00 grams of H2O into moles of H2O like this:
10.00 grams H2O x 1 mole H2O
18.015 grams H2O
We solve this equation by doing 10.00/18.015. (That is 10 divided by 18.015 in case it is hard to read.) The calculator says that 10.00/18.015 = 0.55509. If you look in the equation above, you will see that we have grams on the top (in the "10.00 grams H2O") and on the bottom (in the "18.015 grams H2O"). This means that the grams cancel and vanish. So we are left with mole as the unit. And we already calculated
10/18.015 = 0.55509. When we add the unit of mole to this answer, we have:
0.55509 mole H2O.
Now our amount of H2O is ready to be put into an equation, so let's set it aside for a moment. Now let's look at the coefficients in the equation we were given in the problem:
4 NH3 + 5 O2 --> 4NO + 6H2O
The word coefficient refers to the number right before the compound or element. So in other words, NH3 has a coefficient of 4. O2 has a coefficient of 5. NO has a coefficient of 4, and H2O has a coefficient of 6. These coefficients mean "the number of moles needed to make another substance". The coefficient of O2 is 5, and the coefficient of H2O is 6, so we can interpret these coefficients as "we need 5 moles of O2 to produce 6 moles of H2O". These coefficients are going to be very important in our next equation.
Let's look at how we set up our next equation. We start with the moles of H2O and we want to get moles of O2. Since we start with moles of H2O, we put the coefficient of H2O on the bottom of the coefficients. This way, the word "H2O" will cancel since it's on the top (in the "moles of H2O that we calculated") and on the bottom (in the "coefficient of H2O"). We will be left with "moles of O2" as our unit once we have put in the values and done the calculation. Our equation looks like this:
Moles of H2O that we calculated x coefficient of O2
coefficient of H2O
We know the moles of H2O that we calculated. If you remember, we calculated that 10.00 grams of H2O is equal to 0.55509 mole H2O. So we put "0.55509 mole H2O" in the equation instead of "moles of H2O that we calculated". The equation now looks like this:
0.55509 mole H2O x coefficient of O2
coefficient of H2O
Now let's remember the coefficient of H2O in the equation we were given. Remember that we found the coefficient of H2O in the equation 4 NH3 + 5 O2 --> 4NO + 6H2O. The coefficient for H2O is 6. So we put 6 into our equation instead of "coefficient of H2O". Our equation looks like this:
0.55509 mole H2O x coefficient of O2
Now let's remember the coefficient of O2 in the equation we were given. Remember that we found the coefficient of O2 in the equation 4 NH3 + 5 O2 --> 4NO + 6H2O. The coefficient for O2 is 5. So we put 5 into our equation instead of "coefficient of O2". Our equation looks like this:
0.55509 mole H2O x 5
Now we can multiply 0.55509 x (5/6). The calculator says that 0.55509 x (5/6) = 0.46258. But what does this number mean? This is the moles of O2. If the question had asked for the moles of O2, we could stop here. But the question asks us for the grams of O2. So we have to convert 0.46258 moles of O2 to grams of O2.
How do we convert the moles of O2 to grams of O2? We do this by finding the molar mass of O2. To find the molar mass, we go to the periodic table and look for the atomic mass of O. The atomic mass of O is 15.999. Remember that this is the atomic mass of one O, but we have 2 Os in O2. (We know because the O has a subscript of 2 in O2). So we need to multiply 15.999 x 2 in order to find the molar mass of O2. The calculator says that 15.999 x 2 = 31.998. Thus, we know:
Molar mass of O2 = 31.998 grams of O2 in one mole of O2
Now we can find the number of grams of O2 in 0.46258 mole of O2. We set up the equation like this:
0.46258 mole O2 x 31.998 grams O2
1 mole O2
We solve this equation by multiplying straight across. In other words, we do 0.46258 x 31.998. The calculator says that 0.46258 x 31.998 = 14.80. Notice that the "mole O2" is on the top and the bottom, so it cancels out and we are left with the unit "grams O2". So our answer is 14.80 grams of O2.
Final Answer: 14.80 grams of O2 are required to make 10.00 grams of H2O.