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Question 1189162: Rick combines 8 atoms of hydrogen and 4 atoms of oxygen to make 4 molecules of water. Write a direct variation equation that relates atoms of oxygen O to atoms of hydrogen H. How many hydrogen atoms does Rick need to form water molecules using 32 oxygen atoms? Graph the variation with hydrogen along the x-axis.
Found 3 solutions by Alan3354, Theo, greenestamps:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Rick combines 8 atoms of hydrogen and 4 atoms of oxygen to make 4 molecules of water. Write a direct variation equation that relates atoms of oxygen O to atoms of hydrogen H.
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O = H/2
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How many hydrogen atoms does Rick need to form water molecules using 32 oxygen atoms?
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O = 2H ---> 64
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Graph the variation with hydrogen along the x-axis.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the direct variation formula is y = k * x
you start with:
4 molecules of water is equal to 8 atoms of hydrogen combined with 4 atoms of oxygen.
if you divide both sides of this equation by 4, you get:
1 molecule of water is equal to 2 atoms of hydrogen combined with 1 atom of oxygen.
that means that 1 molecule of water contains 3 atoms, 2 of which are hydrogen and 1 of which is oxygen.
your formula of y = k * x starts off as:
4 = k * 12
4 is your y which is equal to 4 molecules of water.
12 is your x which is equal to 8 atoms of hydrogen combined with 4 atoms of oxygen for a total of 12 atoms.
you solve for k to get:
k = 4/12 = 1/3.
your direct variation formula becomes:
y = 1/3 * x.
when the number of hydrogen atoms is 32, they are combined with 16 atoms of oxygen to get a total of 48 atoms.
your equation becomes y = 1/3 * 48.
solve for y to get y = 16.
when you have 32 atoms of hydrogen, that is combined with 16 atoms of oxygen to get 16 molecules of water.
you could also solve this in the following manner, which doesn't combine the atoms of hydrogen with the atoms of oxygen.
you start with:
y = k * x
y is equal to 4 molecules of water, which we'll call 4w.
x is equal to 8 atoms of hydrogen combined with 4 atoms of oxygen which we'll call 8h + 4o.
y = k * x becomes:
4w = k * (8h + 4o)
w equals one molecule of water.
h = one atom of hydrogen.
o = one atom of oxygen.
solve for k to get:
k = 4w / (8h + 3o)
divide numerator and denominator of the right side of this equation by 4 to get:
k = w / (2h + o)
your direct variation equation becomes:
y = w / (2h + o) * x
when y = 4w and x = (8h + 4o), the equation becomes:
4w = w / (2h + o) * (8h + 4o)
factor (8h + 4o) to have your equation becomes:
4w = w / (2h + o) * 4 * (2h + o)
simplify to get:
4w = 4w, confirming the value of k is correct.
when h becomes 32h, then o becomes 16o and the formula becomes:
y = k * (32h + 16o) which becomes:
y = w / (2h + o) * (32h + 16o)
factor (32h + 16o) to make your equation become:
y = w / (2h + o) * 16 * (2h + o)
solve for y to get:
y = 16w
same answer:
when you have 32 atoms of hydrogen, you get 16 molecules of water that are equal to 32 atoms of hydrogen combined with 16 atoms of oxygen.
the first thing i did above was simpler, because 8 atoms of hydrogen plus 4 atoms of oxygen equals 12 total atoms.
the second thing i did was to show you that, even if you didn't combine hydrogen and oxygen atoms together, you'd get the same answer.
go with the first thing i did that was:
y = k * x becomes:
4 = k * 12.
you solve for k to get:
k = 1/3
your equation becomes:
y = 1/3 * x
when x = 48 total atoms (32 hydrogen plus 16 oxygen), you get:
y = 1/3 * 48 = 16.
you graph:
y = 1/3 * x, which is shown below:
x represents the total number of atoms in 1 molecule of water, which is 3.
y represents the total number of molecules of water.
when you have 12 atoms, 8 of which are hydrogen and 4 of which are oxygen, you get 4 molecules of water.
that's why the coordinate point is (12,4).
that's a total of 12 atoms to 4 molecules of water, 8 of the 12 atoms being hydrogen and 4 of the 12 atoms being oxygen.
when you have a total of 48 atoms, 32 of which are hydrogen and 16 of which are oxygen, you get 16 molecules of water.
that's represented by the coordinate point of (48,16).
let me know if you have any questions.
theo
Answer by greenestamps(13200)  (Show Source):
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