Certainly! Let's go through the conversion step by step.
We start with the given measurement:
[tex]\[ 1.8 \times 10^7 \frac{\text{mol}}{\text{kg} \cdot m^2} \][/tex]
We need to convert this measurement from [tex]\(\text{mol}/(\text{kg} \cdot m^2)\)[/tex] to [tex]\(\text{mol}/(\text{g} \cdot cm^2)\)[/tex].
### Step-by-Step Solution:
1. Understand the Units Involved:
- 1 kilogram (kg) is equal to 1000 grams (g).
- 1 meter squared ([tex]\(m^2\)[/tex]) is equal to [tex]\(100 \times 100 = 10,000\)[/tex] centimeters squared ([tex]\(cm^2\)[/tex]).
2. Convert Kilograms to Grams:
- Since we have kilograms in the denominator, we need to convert them to grams.
- To convert kg to g, multiply by [tex]\(1000\)[/tex]:
[tex]\[
1 \, \text{kg} = 1000 \, \text{g}
\][/tex]
- Therefore, every kg in the denominator can be replaced with [tex]\(1000\)[/tex] g.
3. Convert Square Meters to Square Centimeters:
- Since we have square meters in the denominator, we need to convert them to square centimeters.
- To convert [tex]\(m^2\)[/tex] to [tex]\(cm^2\)[/tex], multiply the conversion by [tex]\(10,000\)[/tex] because there are [tex]\(10,000\)[/tex] square centimeters in a square meter:
[tex]\[
1 \, \text{m}^2 = 10,000 \, \text{cm}^2
\][/tex]
4. Combine the Conversion Factors:
- To adjust from [tex]\(\frac{\text{mol}}{\text{kg} \cdot m^2}\)[/tex] to [tex]\(\frac{\text{mol}}{\text{g} \cdot cm^2}\)[/tex], we need to adjust for both kg to g and [tex]\(m^2\)[/tex] to [tex]\(cm^2\)[/tex]:
[tex]\[
\frac{1 \, \text{kg}}{1} = \frac{1000 \, \text{g}}{1}
\][/tex]
[tex]\[
\frac{1 \, \text{m}^2}{1} = \frac{10,000 \, \text{cm}^2}{1}
\][/tex]
Therefore, the combined conversion factor is:
[tex]\[
\frac{1000 \, \text{g}}{10,000 \, \text{cm}^2} = \frac{1000}{10,000} = 0.1
\][/tex]
5. Apply the Conversion Factor:
- Multiply the given value by the conversion factor:
[tex]\[
1.8 \times 10^7 \frac{\text{mol}}{\text{kg} \cdot m^2} \times \frac{0.1 \, \text{g} \cdot cm^2}{1 \, \text{kg} \cdot m^2}
\][/tex]
Performing the multiplication:
[tex]\[
1.8 \times 10^7 \times 0.1 = 1.8 \times 10^6 = 1,800,000
\][/tex]
### Final Result:
[tex]\[
1.8 \times 10^7 \frac{\text{mol}}{\text{kg} \cdot m^2} = 1,800,000 \frac{\text{mol}}{\text{g} \cdot cm^2}
\][/tex]
Therefore, the converted measurement is:
[tex]\[
1,800,000 \frac{\text{mol}}{\text{g} \cdot cm^2}
\][/tex]
