Assume for this problem that 20 drops exactly equal 1 mL. A student places 2 drops of 12.0 M HCl in a test tube. How many drops of water must she add to the test tube to obtain a solution in which HCl has a concentration of 1.20 M?
A 32 drops
B 20 drops
C 12 drops
D 18 drops
The correct answer and explanation is :
To solve this dilution problem, we use the dilution formula:
[
M_1V_1 = M_2V_2
]
where:
- ( M_1 = 12.0 ) M (initial concentration of HCl)
- ( V_1 = 2 ) drops (initial volume of HCl)
- ( M_2 = 1.20 ) M (final concentration of HCl)
- ( V_2 ) = final total volume (HCl + water)
Step 1: Find Final Volume ( V_2 )
Rearrange the equation to solve for ( V_2 ):
[
V_2 = \frac{M_1V_1}{M_2}
]
Substituting values:
[
V_2 = \frac{(12.0 \text{ M}) (2 \text{ drops})}{1.20 \text{ M}}
]
[
V_2 = \frac{24.0}{1.20} = 20 \text{ drops}
]
Step 2: Find Amount of Water to Add
Since the final volume ( V_2 ) includes both the original HCl solution and the added water, the amount of water needed is:
[
\text{Water to add} = V_2 – V_1
]
[
= 20 \text{ drops} – 2 \text{ drops}
]
[
= 18 \text{ drops}
]
Answer:
The correct answer is D) 18 drops.
Explanation:
The student starts with 2 drops of concentrated HCl (12.0 M). To dilute it to 1.20 M, the total volume must be 20 drops. Since the initial solution already contains 2 drops of HCl, the remaining 18 drops must come from water. This maintains the ratio required for dilution while keeping the final concentration at 1.20 M. Thus, the student must add 18 drops of water to achieve the desired concentration.