Question

Use dimensional analysis to solve the following problems. Pay attention to correct use of units and correct use of significant figures in calculations. Please show work!

Convert 3.00 x 10^21 atoms of copper to moles.

Convert 2.25 x 10^18 molecules of carbon dioxide to moles.

Answer 1

Step-by-step explanation:

by definition, 1 mole contains 6.02 x 10^23 of atoms (for elements) or molecules (for compounds)

3.00 x 10^21 atoms of copper / 6.02 x 10^23 of atoms

= 0.004983 moles of copper

= 4.98 x 10^(-3) moles of copper

2.25 x 10^18 molecules of carbon dioxide / 6.02 x 10^23 of molecules

= 0.000003737 moles of carbon dioxide

= 3.74 x 10^(-6) moles of carbon dioxide

Answer 2

1) 0.00498 mol Cu.

2) 0.00000374 mol CO₂

Step-by-step explanation:

Question 1)

We want to convert 3.00 * 10²¹ copper atoms into moles. Note that 3.00 is three significant figures.

Recall that by definition, one mole of a substance has exactly 6.022 * 10²³ amount of that substance. In other words, we have the ratio:

`\displaystyle \frac{1\text{ mol}}{6.022* 10^(23) \text{ Cu}}`

We are given 3.00 * 10²¹ Cu. To cancel out the Cu, we can multiply it by our above ratio with Cu in the denominator. Hence:

`\displaystyle 3.00 * 10^(21) \text{ Cu} \cdot \frac{1\text{ mol Cu}}{6.022* 10^(23) \text{ Cu}}`

Cancel like terms:

`=\displaystyle 3* 10^(21) \cdot \frac{1\text{ mol Cu}}{6.022* 10^(23) }`

Simplify:

`\displaystyle = \frac{3\text{ mol Cu}}{6.022 * 10^(2)}`

Use a calculator:

`= 0.004981... \text{ mol Cu}`

Since the resulting answer must have three significant figures:

`= 0.00498\text{ mol Cu}`

So, 3.00 * 10²¹ copper atoms is equivalent to approximately 0.00498 moles of copper.

Question 2)

We want to convert 2.25 * 10¹⁸ molecules of carbon dioxide into moles. Note that 2.25 is three significant digits.

By definition, there will be 6.022 * 10²³ carbon dioxide molecules in one mole of carbon dioxide. Hence:

`\displaystyle \frac{6.022 * 10^(23) \text{ CO$_2$}}{1\text{ mol CO$_2$}}`

To cancel the carbon dioxide from 2.25 * 10¹⁸, we can multiply it by the above ratio with the carbon dioxide in the denominator. Hence:

`\displaystyle 2.25* 10^(18) \text{ CO$_2$} \cdot \frac{1\text{ mol CO$_2$}}{6.022* 10^(23) \text{ CO$_2$}}`

Cancel like terms:

`\displaystyle= 2.25* 10^(18) \cdot \frac{1\text{ mol CO$_2$}}{6.022* 10^(23)}`

Simplify:

`\displaystyle = \frac{2.25 \text{ mol CO$_2$}}{6.022* 10^5}}`

Use a calculator:

`=0.000003736...\text{ mol CO$_2$}`

Since the resulting answer must have three significant figures:

`= 0.00000374\text{ mol CO$_2$}`

So, 2.25 * 10¹⁸ molecules of carbon dioxide is equivalent to approximately 0.00000374 moles of carbon dioxide.