A sample of #C_3H_8# has #6.72 times 10^24# #H# atoms. How many carbon atoms does the sample contain?

Question

Wyatt Atkins · Accepted Answer

Would this not simply be #3/8xx6.72xx10^24# #"carbon atoms"#?

If we have #6.72xx10^24# hydrogen atoms in the propane sample, surely given the formula of propane, i.e. #C_3H_8#, there would be #3/8xx6.72xx10^24# individual carbon atoms...... The numbers here are pretty irrelevant (meaning that I could choose any number), save that we also know that #"Avogadro's Number"# of #"propane molecules"#, #6.022xx10^23# individual molecules of propane, has a mass of #44.1*g#. Can you tell us the mass of the given quantity of propane in the question?

Avery Adams · Answer

undefined The ratio of hydrogen atoms to carbon atoms in C3H8 is 8:3. So, if there are 6.72 x 10^24 hydrogen atoms, there would be (6.72 x 10^24) / 8 = 8.4 x 10^23 carbon atoms in the sample.

Natalie Anton · Answer

undefined To find the number of carbon atoms in the sample of $ C_3H_8 $, we first need to determine the ratio of hydrogen atoms to carbon atoms in one molecule of $ C_3H_8 $.

Given that each molecule of $ C_3H_8 $ contains 8 hydrogen atoms and 3 carbon atoms, the ratio of hydrogen atoms to carbon atoms is $ 8:3 $.

Next, we can use the given number of hydrogen atoms ($ 6.72 \times 10^{24} $) to find the number of carbon atoms.

Using the ratio $ 8:3 $, we can set up a proportion:

$$
\frac{6.72 \times 10^{24} \text{ H atoms}}{x \text{ C atoms}} = \frac{8}{3}
$$

Where $ x $ represents the number of carbon atoms.

Solving for $ x $:

$$
x = \frac{(6.72 \times 10^{24} \text{ H atoms}) \times 3}{8}
$$

$$
x = \frac{6.72 \times 3}{8} \times 10^{24}
$$

$$
x = 2.52 \times 10^{24}
$$

So, the sample of $ C_3H_8 $ contains $ 2.52 \times 10^{24} $ carbon atoms.