Which equation shows the proper setup to find the volume of a $0.250 M CaCl _2$ solution that contains 39.5 g or $CaCl _2$?
$0.250 M CaCl _2=\frac{39.5 g CaCl _2}{V}$
$V=39.5 g CaCl _2 \times \frac{1 mol CaCl }{110.98 g CaCl _2} \times \frac{1 L}{0.250 mol CaCl _2}$
$V=\frac{39.5 g CaCl _2}{0.250 M CaCl _2}$
Answer (2)
Convert the mass of C a C l 2 to moles using its molar mass: m o l es = 110.98 g / m o l 39.5 g .
Use the definition of molarity to relate moles, volume, and molarity: M o l a r i t y = V o l u m e m o l es .
Rearrange the molarity formula to solve for volume: V o l u m e = M o l a r i t y m o l es .
The correct equation that represents this setup is: V = 39.5 g C a C l 2 × 110.98 g C a C l 2 1 m o lC a Cl × 0.250 m o lC a C l 2 1 L .
Explanation
Problem Analysis We are asked to find the correct equation to calculate the volume of a 0.250 M C a C l 2 solution that contains 39.5 g of C a C l 2 . We will use the definition of molarity to find the correct setup.
Calculating Moles of Calcium Chloride First, we need to find the number of moles of C a C l 2 . We can do this by dividing the given mass by the molar mass of C a C l 2 . The molar mass of C a C l 2 is approximately 110.98 g / m o l . Therefore, the number of moles of C a C l 2 is: m o l es = m o l a r ma ss ma ss = 110.98 g / m o l 39.5 g = 0.3559 m o l
Calculating the Volume Next, we use the definition of molarity, which is: M o l a r i t y = V o l u m e ( in L i t ers ) m o l es We are given the molarity as 0.250 M , and we have calculated the number of moles as 0.3559 m o l . We need to solve for the volume. Rearranging the formula, we get: V o l u m e = M o l a r i t y m o l es Substituting the values, we have: V o l u m e = 0.250 M 0.3559 m o l = 1.4236 L Now let's examine the given options to see which one matches our calculation.
Evaluating the Options Option 1: 0.250 MC a C l 2 = V 39.5 g C a C l 2 This equation can be rearranged to V = 0.250 MC a C l 2 39.5 g C a C l 2 . This setup is missing the conversion from grams to moles, so it is not correct.
Option 2: V = 39.5 g C a C l 2 × 110.98 g C a C l 2 1 m o lC a Cl × 0.250 m o lC a C l 2 1 L This equation correctly converts grams to moles and then uses the molarity to find the volume. This is the correct setup.
Option 3: V = 0.250 MC a C l 2 39.5 g C a C l 2 This is the same as option 1 and is missing the conversion from grams to moles, so it is not correct.
Final Answer Therefore, the correct equation is: V = 39.5 g C a C l 2 × 110.98 g C a C l 2 1 m o lC a Cl × 0.250 m o lC a C l 2 1 L
Examples
In chemistry, calculating the volume of a solution with a specific molarity is crucial for preparing reagents for experiments. For example, if you need to create a specific concentration of a salt solution to study its effect on reaction rates, you must accurately calculate the volume of the solution required to achieve the desired molarity. This calculation ensures that your experiment uses the correct amount of reactants, leading to reliable and reproducible results. Accurately preparing solutions is a fundamental skill in any chemistry lab, ensuring the validity of experimental data and the success of chemical processes.
To find the volume of a 0.250 M CaCl₂ solution from 39.5 g of CaCl₂, convert grams to moles using the molar mass of CaCl₂ which is 110.98 g/mol. The correct setup for the calculation is given by the equation: V=39.5 g CaCl₂ × (1 mol CaCl₂/110.98 g CaCl₂) × (1 L/0.250 mol CaCl₂).
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