To solve the problem of finding the masses of calcium chloride ([tex]\( CaCl_2 \)[/tex]) and water in a mixture where the total mass is 424.1 grams and [tex]\( CaCl_2 \)[/tex] makes up 38.5% of the mixture by mass, follow these steps:
1. Identify the given values:
- Total mass of the mixture ([tex]\( M \)[/tex]): 424.1 grams
- Percentage of [tex]\( CaCl_2 \)[/tex] by mass ([tex]\( P \)[/tex]): 38.5%
2. Calculate the mass of [tex]\( CaCl_2 \)[/tex]:
- The percentage given tells us how much of the total mass is [tex]\( CaCl_2 \)[/tex]. To find this, convert the percentage to a decimal by dividing by 100.
- [tex]\( P / 100 = 38.5 / 100 = 0.385 \)[/tex]
- Multiply this decimal by the total mass of the mixture to get the mass of [tex]\( CaCl_2 \)[/tex]:
[tex]\[
\text{Mass of } CaCl_2 = P \times M = 0.385 \times 424.1 = 163.2785 \text{ grams}
\][/tex]
3. Calculate the mass of water:
- The mass of the water in the mixture can be found by subtracting the mass of [tex]\( CaCl_2 \)[/tex] from the total mass of the mixture:
[tex]\[
\text{Mass of water} = M - \text{Mass of } CaCl_2 = 424.1 - 163.2785 = 260.8215 \text{ grams}
\][/tex]
Therefore, the masses of the components in the mixture are:
- The mass of [tex]\( CaCl_2 \)[/tex] is 163.2785 grams.
- The mass of water is 260.8215 grams.
