Question

1. 15 moles
2. 0.35 mole

how many moles are in the number of molecules below?

1. $6.02 \times 10^{23}$
2. $1.204 \times 10^{24}$
3. $1.5 \times 10^{20}$
4. $3.4 \times 10^{26}$
5. $7.5 \times 10^{19}$

Explanation:

To solve for the number of moles from the number of molecules, we use the formula:
$\text{Moles} = \frac{\text{Number of Molecules}}{6.02 \times 10^{23}\ \text{molecules/mol}}$ (Avogadro’s number).

1. For $6.02 \times 10^{23}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{6.02 \times 10^{23}}{6.02 \times 10^{23}}$

Step2: Simplify the expression

$\text{Moles} = 1\ \text{mol}$

2. For $1.204 \times 10^{24}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{1.204 \times 10^{24}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{1.204}{6.02} = 0.2$; $10^{24 - 23} = 10^1$
$\text{Moles} = 0.2 \times 10^1 = 2\ \text{mol}$

3. For $1.5 \times 10^{20}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{1.5 \times 10^{20}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{1.5}{6.02} \approx 0.249$; $10^{20 - 23} = 10^{-3}$
$\text{Moles} \approx 0.249 \times 10^{-3} = 2.49 \times 10^{-4}\ \text{mol}$ (or $0.000249\ \text{mol}$)

4. For $3.4 \times 10^{26}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{3.4 \times 10^{26}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{3.4}{6.02} \approx 0.565$; $10^{26 - 23} = 10^3$
$\text{Moles} \approx 0.565 \times 10^3 = 565\ \text{mol}$ (or $5.65 \times 10^2\ \text{mol}$)

5. For $7.5 \times 10^{19}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{7.5 \times 10^{19}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{7.5}{6.02} \approx 1.246$; $10^{19 - 23} = 10^{-4}$
$\text{Moles} \approx 1.246 \times 10^{-4}\ \text{mol}$ (or $0.0001246\ \text{mol}$)

Final Answers:

1. $\boldsymbol{1\ \text{mol}}$
2. $\boldsymbol{2\ \text{mol}}$
3. $\boldsymbol{\approx 2.5 \times 10^{-4}\ \text{mol}}$ (or $0.00025\ \text{mol}$, rounded)
4. $\boldsymbol{\approx 565\ \text{mol}}$ (or $5.65 \times 10^2\ \text{mol}$)
5. $\boldsymbol{\approx 1.25 \times 10^{-4}\ \text{mol}}$ (or $0.000125\ \text{mol}$, rounded)

Answer:

To solve for the number of moles from the number of molecules, we use the formula:
$\text{Moles} = \frac{\text{Number of Molecules}}{6.02 \times 10^{23}\ \text{molecules/mol}}$ (Avogadro’s number).

1. For $6.02 \times 10^{23}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{6.02 \times 10^{23}}{6.02 \times 10^{23}}$

Step2: Simplify the expression

$\text{Moles} = 1\ \text{mol}$

2. For $1.204 \times 10^{24}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{1.204 \times 10^{24}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{1.204}{6.02} = 0.2$; $10^{24 - 23} = 10^1$
$\text{Moles} = 0.2 \times 10^1 = 2\ \text{mol}$

3. For $1.5 \times 10^{20}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{1.5 \times 10^{20}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{1.5}{6.02} \approx 0.249$; $10^{20 - 23} = 10^{-3}$
$\text{Moles} \approx 0.249 \times 10^{-3} = 2.49 \times 10^{-4}\ \text{mol}$ (or $0.000249\ \text{mol}$)

4. For $3.4 \times 10^{26}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{3.4 \times 10^{26}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{3.4}{6.02} \approx 0.565$; $10^{26 - 23} = 10^3$
$\text{Moles} \approx 0.565 \times 10^3 = 565\ \text{mol}$ (or $5.65 \times 10^2\ \text{mol}$)

5. For $7.5 \times 10^{19}$ molecules:

Step1: Apply the moles formula

$\text{Moles} = \frac{7.5 \times 10^{19}}{6.02 \times 10^{23}}$

Step2: Simplify (divide coefficients and subtract exponents)

$\frac{7.5}{6.02} \approx 1.246$; $10^{19 - 23} = 10^{-4}$
$\text{Moles} \approx 1.246 \times 10^{-4}\ \text{mol}$ (or $0.0001246\ \text{mol}$)

Final Answers:

1. $\boldsymbol{1\ \text{mol}}$
2. $\boldsymbol{2\ \text{mol}}$
3. $\boldsymbol{\approx 2.5 \times 10^{-4}\ \text{mol}}$ (or $0.00025\ \text{mol}$, rounded)
4. $\boldsymbol{\approx 565\ \text{mol}}$ (or $5.65 \times 10^2\ \text{mol}$)
5. $\boldsymbol{\approx 1.25 \times 10^{-4}\ \text{mol}}$ (or $0.000125\ \text{mol}$, rounded)