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## Problem 3 Solution

```
(a) 313 carbon atoms and 1252 hydrogen atoms
(b) Not if all of the atoms are involved in methane molecules.
```

### Solution Steps for Part (a):

If a sample of methane contains 1565 atoms, how much carbon and hydrogen are present?

### Answer:

This is different from the last problem because we are given the total number of atoms instead of the amount present of one of them. What do we know?

carbon + hydrogen = 1565
and
.

Let's cross multiply this proportion as usual to get:

4 carbon = hydrogen.

So, we can substitute 4 carbons in for the hydrogen in the first equation:

carbon + 4 carbon = 1565

Put the carbons together: (4 and 1 makes 5)

5 carbon = 1565
and divide both sides by 5
carbon = 313.

So what's left must be hydrogen: 1565 - 313 = 1252.

### Solution Steps for Part (b):

Can a sample contain 1566 atoms?

### Answer:

Look at the work from part (a): We know that the total number of atoms must be divisible by 5.

Think about what a ratio tells you when you can't have fractional parts of the items: The items must come in groups of 5 -- 1 carbon for every 4 hydrogens in this case.

Using this idea, there can't be 1566 atoms because 1566 is not divisible by 5 because 5 carbon = 1565(total). Try it on your calculator; do you get a whole number? No!

Next Try It Out Problem.

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