A sample of propane(c3h8)has 3.84x10^24 H atoms.

a) how many carbon atoms does the sample contain?
b) what is the total mass of the sample?

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a) Well, since propane has a ratio of 3 hydrogen atoms to 1 carbon atom, we can use simple math to find the number of carbon atoms. If we have 3.84x10^24 hydrogen atoms, we can divide that by 3 to get the number of carbon atoms. But let's not test my math skills here, a mathematician might get offended. So, we'll just punch the numbers in and... Voila! The sample contains approximately 1.28x10^24 carbon atoms.

b) Ah, mass! This calls for some heavy calculations. Or maybe not so heavy, let's keep it light and fun! The molar mass of propane is approximately 44.1 grams per mole. Since we know the number of carbon atoms now, we need to find the moles of carbon and multiply it by the molar mass and... boom! We've got the mass of the sample. The total mass of the sample is roughly 56.4 grams. Don't worry, it's not as heavy as my jokes!

To answer these questions, we first need to understand the molecular formula of propane (C3H8).

a) In one molecule of propane (C3H8), there are three carbon (C) atoms. So, to find the number of carbon atoms in the sample, we need to know the ratio of carbon to hydrogen atoms in the molecular formula.

The molecular formula for propane (C3H8) means that for every three carbon atoms, there are eight hydrogen atoms. Now, we know that the sample has 3.84x10^24 hydrogen atoms. To calculate the number of carbon atoms, we can use a ratio:

(Number of carbon atoms in the sample) / (Number of hydrogen atoms in the sample) = (Number of carbon atoms in one molecule of propane) / (Number of hydrogen atoms in one molecule of propane)

Let's calculate it:

(Number of carbon atoms in the sample) / (3.84x10^24 H atoms) = (3 carbon atoms in one molecule of propane) / (8 H atoms in one molecule of propane)

Cross-multiplying, we get:

(Number of carbon atoms in the sample) = (3 carbon atoms in one molecule of propane) x (3.84x10^24 H atoms) / (8 H atoms in one molecule of propane)

Now, we can substitute the known values and calculate the answer:

(Number of carbon atoms in the sample) = (3 x 3.84x10^24) / 8

b) To find the total mass of the sample, we need to know the molar mass of propane (C3H8) and use it to convert the number of moles of propane to grams. The molar mass of propane can be found by summing up the atomic masses of the individual atoms in the formula.

To calculate the molar mass of propane:

Molar mass of C3H8 = (3 x atomic mass of carbon) + (8 x atomic mass of hydrogen)

To get the atomic masses of carbon and hydrogen, we can refer to the periodic table or use reliable sources. For example, the atomic mass of carbon (C) is approximately 12.01 grams per mole (g/mol), and the atomic mass of hydrogen (H) is approximately 1.008 g/mol.

Therefore:

Molar mass of C3H8 = (3 x 12.01 g/mol) + (8 x 1.008 g/mol)

Now, we have calculated the molar mass of propane (C3H8).

Finally, to find the total mass of the sample, we need to convert the number of moles of propane to grams. We can use the relationship between moles and mass:

Mass = Number of moles x Molar mass

To find the number of moles, we can use Avogadro's number, which states that 1 mole of any substance contains 6.022 x 10^23 entities.

Number of moles = Number of entities / Avogadro's number

Given the number of carbon atoms in the sample from part (a), we can use the same formula to calculate the number of moles of propane (C3H8):

Number of moles = (Number of carbon atoms in the sample) / Avogadro's number

Once we have the number of moles, we can substitute it into the mass equation and calculate the total mass of the sample.

From the formula (C3H8) [please use capital letters for element symbols] we see that there are 3 C atoms for 8 H atoms. If we had 16 H atoms there would be 6 C atoms for example.

Thus is there are 3.84x10^24 H atoms.

a) then there are (3/8)x3.84x10^24 C atoms

b) there are a couple of ways to do this.
If the sample contains 3.84x10^24 H atoms and each molecule contains 8 H atoms then there are 3.84x10^24/8 molecules of propane. Each mole contains 6 x 10^23 molecules so there are
3.84x10^24/(8 x 6 x 10^23 )moles

the molar mass of propane is

(3x12)+(8x1) g mole^-1

hence find the mass as

mass= molar mass x number of moles