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

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:

$\displaystyle \frac{1\text{ mol}}{6.022\times 10^{23} \text{ Cu}}$

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:

$\displaystyle 3.00 \times 10^{21} \text{ Cu} \cdot \frac{1\text{ mol Cu}}{6.022\times 10^{23} \text{ Cu}}$

Cancel like terms:

$=\displaystyle 3\times 10^{21} \cdot \frac{1\text{ mol Cu}}{6.022\times 10^{23} }$

Simplify:

$\displaystyle = \frac{3\text{ mol Cu}}{6.022 \times 10^{2}}$

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:

$\displaystyle \frac{6.022 \times 10^{23} \text{ CO _2 }}{1\text{ mol CO _2 }}$

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:

$\displaystyle 2.25\times 10^{18} \text{ CO _2 } \cdot \frac{1\text{ mol CO _2 }}{6.022\times 10^{23} \text{ CO _2 }}$

Cancel like terms:

$\displaystyle= 2.25\times 10^{18} \cdot \frac{1\text{ mol CO _2 }}{6.022\times 10^{23}}$

Simplify:

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

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.

Answer 2

Answer:

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