To convert the measurement [tex]\(3.1 \times 10^6 \frac{\text{mol}}{\text{kg} \cdot \text{m}^2}\)[/tex] to [tex]\(\frac{\text{mol}}{\text{g} \cdot \text{cm}^2}\)[/tex], follow these steps:
1. Understand the Conversion Factors:
- We need to convert kilograms (kg) to grams (g).
- We also need to convert square meters (m²) to square centimeters (cm²).
2. Conversion from kilograms to grams:
- 1 kilogram (kg) equals 1000 grams (g).
- Therefore, we use the conversion factor [tex]\(1 \text{ kg} = 1000 \text{ g}\)[/tex].
3. Conversion from square meters to square centimeters:
- 1 meter (m) equals 100 centimeters (cm).
- Therefore, [tex]\(1 \text{ m}^2\)[/tex] is [tex]\( (100 \text{ cm})^2 = 10,000 \text{ cm}^2 \)[/tex].
4. Apply the Conversion Factors:
- We need to convert the units in the denominator from kg to g and from [tex]\( \text{m}^2 \)[/tex] to [tex]\( \text{cm}^2 \)[/tex].
- Multiply the original value by the conversion factors, noting that conversion factors for denominator units will result in division.
5. Convert the Units:
Given value: [tex]\(3.1 \times 10^6 \frac{\text{mol}}{\text{kg} \cdot \text{m}^2}\)[/tex].
- Convert kg to g:
- As 1 kg = 1000 g, this implies that [tex]\(\frac{1}{1000}\)[/tex] for kg to g conversion.
- Convert [tex]\( \text{m}^2 \)[/tex] to [tex]\( \text{cm}^2 \)[/tex]:
- As 1 m² = 10,000 cm², this implies that [tex]\(\frac{1}{10,000}\)[/tex] for m² to cm² conversion.
Therefore,
[tex]\[
3.1 \times 10^6 \frac{\text{mol}}{\text{kg} \cdot \text{m}^2} \times \frac{1}{1000} \times \frac{1}{10000} = 3.1 \times 10^6 \times \frac{1}{10000000} \frac{\text{mol}}{\text{g} \cdot \text{cm}^2}
\][/tex]
6. Calculate the Final Value:
[tex]\[
3.1 \times 10^6 \times \frac{1}{10^7} = \frac{3.1}{10} = 0.31
\][/tex]
So, the converted measurement is:
[tex]\[
3.1 \times 10^6 \frac{\text{mol}}{\text{kg} \cdot \text{m}^2} = 0.31 \frac{\text{mol}}{\text{g} \cdot \text{cm}^2}
\][/tex]
