Answer:
1) 0.00498 mol Cu.
2) 0.00000374 mol CO₂
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:
[tex]\displaystyle \frac{1\text{ mol}}{6.022\times 10^{23} \text{ Cu}}[/tex]
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:
[tex]\displaystyle 3.00 \times 10^{21} \text{ Cu} \cdot \frac{1\text{ mol Cu}}{6.022\times 10^{23} \text{ Cu}}[/tex]
Cancel like terms:
[tex]=\displaystyle 3\times 10^{21} \cdot \frac{1\text{ mol Cu}}{6.022\times 10^{23} }[/tex]
Simplify:
[tex]\displaystyle = \frac{3\text{ mol Cu}}{6.022 \times 10^{2}}[/tex]
Use a calculator:
[tex]= 0.004981... \text{ mol Cu}[/tex]
Since the resulting answer must have three significant figures:
[tex]= 0.00498\text{ mol Cu}[/tex]
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:
[tex]\displaystyle \frac{6.022 \times 10^{23} \text{ CO$_2$}}{1\text{ mol CO$_2$}}[/tex]
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:
[tex]\displaystyle 2.25\times 10^{18} \text{ CO$_2$} \cdot \frac{1\text{ mol CO$_2$}}{6.022\times 10^{23} \text{ CO$_2$}}[/tex]
Cancel like terms:
[tex]\displaystyle= 2.25\times 10^{18} \cdot \frac{1\text{ mol CO$_2$}}{6.022\times 10^{23}}[/tex]
Simplify:
[tex]\displaystyle = \frac{2.25 \text{ mol CO$_2$}}{6.022\times 10^5}}[/tex]
Use a calculator:
[tex]=0.000003736...\text{ mol CO$_2$}[/tex]
Since the resulting answer must have three significant figures:
[tex]= 0.00000374\text{ mol CO$_2$}[/tex]
So, 2.25 * 10¹⁸ molecules of carbon dioxide is equivalent to approximately 0.00000374 moles of carbon dioxide.
