Answer :
Certainly! Let's go through the solution step-by-step:
We start with the given value:
[tex]\[ 1.9 \times 10^4 \frac{\text{g}}{\text{mol} \cdot \text{L}} \][/tex]
We need to convert this value to:
[tex]\[ \frac{\text{kg}}{\text{mol} \cdot \text{dL}} \][/tex]
### Step-by-Step Conversion
1. Convert grams to kilograms:
- We know that [tex]\(1 \text{ gram} = 0.001 \text{ kilograms}\)[/tex].
- Thus, we can convert [tex]\(1.9 \times 10^4 \text{ grams}\)[/tex] to kilograms:
[tex]\[
1.9 \times 10^4 \times 0.001 = 1.9 \times 10 \text{ kilograms}
\][/tex]
2. Convert liters to deciliters:
- We know that [tex]\(1 \text{ liter} = 10 \text{ deciliters} (dL)\)[/tex].
- Thus, converting the denominator from liters to deciliters:
[tex]\[
\frac{1}{L} \to \frac{1}{10 dL} = 0.1 \frac{1}{dL}
\][/tex]
3. Combine the conversions:
- Multiply the converted kilograms value by the factor for converting liters to deciliters:
[tex]\[
\left(1.9 \times 10 \frac{\text{kg}}{\text{mol} \cdot \text{L}}\right) \times 10 = 190 \frac{\text{kg}}{\text{mol} \cdot \text{dL}}
\][/tex]
So, putting this all together, we end up with:
[tex]\[ 1.9 \times 10^4 \frac{\text{g}}{\text{mol} \cdot \text{L}} = 190 \frac{\text{kg}}{\text{mol} \cdot \text{dL}} \][/tex]
Therefore, the final converted value is:
[tex]\[ 190 \frac{\text{kg}}{\text{mol} \cdot \text{dL}} \][/tex]
We start with the given value:
[tex]\[ 1.9 \times 10^4 \frac{\text{g}}{\text{mol} \cdot \text{L}} \][/tex]
We need to convert this value to:
[tex]\[ \frac{\text{kg}}{\text{mol} \cdot \text{dL}} \][/tex]
### Step-by-Step Conversion
1. Convert grams to kilograms:
- We know that [tex]\(1 \text{ gram} = 0.001 \text{ kilograms}\)[/tex].
- Thus, we can convert [tex]\(1.9 \times 10^4 \text{ grams}\)[/tex] to kilograms:
[tex]\[
1.9 \times 10^4 \times 0.001 = 1.9 \times 10 \text{ kilograms}
\][/tex]
2. Convert liters to deciliters:
- We know that [tex]\(1 \text{ liter} = 10 \text{ deciliters} (dL)\)[/tex].
- Thus, converting the denominator from liters to deciliters:
[tex]\[
\frac{1}{L} \to \frac{1}{10 dL} = 0.1 \frac{1}{dL}
\][/tex]
3. Combine the conversions:
- Multiply the converted kilograms value by the factor for converting liters to deciliters:
[tex]\[
\left(1.9 \times 10 \frac{\text{kg}}{\text{mol} \cdot \text{L}}\right) \times 10 = 190 \frac{\text{kg}}{\text{mol} \cdot \text{dL}}
\][/tex]
So, putting this all together, we end up with:
[tex]\[ 1.9 \times 10^4 \frac{\text{g}}{\text{mol} \cdot \text{L}} = 190 \frac{\text{kg}}{\text{mol} \cdot \text{dL}} \][/tex]
Therefore, the final converted value is:
[tex]\[ 190 \frac{\text{kg}}{\text{mol} \cdot \text{dL}} \][/tex]
