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Chapter 9: Problem 13

Suppose you have \(5.000 \times 10^{24}\) molecules of methane, \(\mathrm{CH}_{4}\). (a) How many moles of methane do you have? (b) How many grams of methane do you have?

Short Answer

Expert verified
(a) There are 8.300 moles of methane. (b) There are 133.1 grams of methane.

Step by step solution

01

Calculate the number of moles of methane

To find the number of moles of methane, divide the given number of molecules by Avogadro's number (6.022 x 10^23 molecules/mol). Number of moles = \( \frac{5.000 \times 10^{24} \ \mathrm{molecules}}{6.022 \times 10^{23} \ \mathrm{molecules/mol}} \)
02

Simplify the calculation

Now, you can simply divide the numbers and cancel out the units to calculate the number of moles. Number of moles = \( \frac{5.000 \times 10^{24}}{6.022 \times 10^{23}} \) = 8.300 moles So there are 8.300 moles of methane.
03

Calculate the grams of methane

Now that we know the number of moles of methane, we can multiply it by the molecular weight of methane (16.04 g/mol) to find the grams of methane. Grams of methane = 8.300 moles × 16.04 g/mol
04

Simplify the calculation and find the final answer

Multiply the numbers and cancel out the units to find the number of grams. Grams of methane = 8.300 moles × 16.04 g/mol = 133.1 g So there are 133.1 grams of methane.

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