The molar mass of calcium chloride ($CaCl_2$) is $110.98 g/mol$. If you were to calculate the number of moles in 23.4 g of $CaCl_2$, which example shows the correct way to set up the calculation?
A. $23.4 g CaCl_2 \times \frac{110.98 g CaCl_2}{1 mole CaCl}$
B. $23.4 g CaCl_2 \times \frac{1 mole CaCl_2}{110.98 g CaCl_2}$
Answer (2)
The problem requires calculating the number of moles of C a C l 2 from a given mass.
The formula to calculate moles is m o l es = m o l a r ma ss ma ss .
The correct setup is 23.4 g C a C l 2 × 110.98 g C a C l 2 1 m o l e C a C l 2 , ensuring the grams unit cancels out.
The final answer is the setup: 23.4 g C a C l 2 × 110.98 g C a C l 2 1 m o l e C a C l 2 .
Explanation
Problem Analysis We are asked to determine the correct setup for calculating the number of moles of C a C l 2 given its mass and molar mass. The molar mass of C a C l 2 is 110.98 g / m o l , and we have 23.4 g of C a C l 2 .
Formula Application To find the number of moles, we use the formula: m o l es = m o l a r ma ss ma ss We need to divide the given mass by the molar mass.
Calculation Setup Substituting the given values, we have: m o l es = 110.98 g / m o l 23.4 g This can be set up as: 23.4 g C a C l 2 × 110.98 g C a C l 2 1 m o l C a C l 2 Notice how the grams ( g ) unit cancels out, leaving us with the unit of moles ( m o l ).
Comparison and Selection Comparing this to the given options, the correct setup is: 23.4 g C a C l 2 × 110.98 g C a C l 2 1 m o l e C a C l 2 The other option is incorrect because it would result in units of g 2 / m o l :
23.4 g C a C l 2 × 1 m o l e C a Cl 110.98 g C a C l 2 = 1 m o l e C a C l 2 23.4 × 110.98 g 2 .
Final Answer Therefore, the correct way to set up the calculation is: 23.4 g C a C l 2 × 110.98 g C a C l 2 1 m o l e C a C l 2
Examples
Imagine you're baking a cake and the recipe calls for a certain number of moles of an ingredient. If you only have the mass of that ingredient, you need to convert it to moles using the molar mass. This problem demonstrates how to correctly set up that conversion, ensuring you use the right amount of each ingredient for your recipe. Similarly, in chemistry, when performing reactions, it's crucial to know the number of moles of each reactant to ensure the reaction proceeds correctly and efficiently. This calculation is fundamental in stoichiometry, which deals with the quantitative relationships between reactants and products in chemical reactions.
The correct setup for calculating the number of moles of calcium chloride ( C a C l 2 ) from 23.4 g is: 23.4 g C a C l 2 × 110.98 g C a C l 2 1 m o l e C a C l 2 . This ensures that the grams cancel out and you get an answer in moles. Therefore, the correct option is B.
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