Question

10.0 ml of a 5.00 m solution was added to 90.0 ml of water. what is the concentration of the diluted solution?
there are 4 variables in the dilution equation. the problem will give three, then you solve for the missing variable.
$c_dv_d = c_cv_c$
$v_c =$ 1 ml $v_d =$ 2 ml $c_c =$ 3 m
$c_d =$? solving for $c_d$ first put in the symbols, then put in the numbers
$c_d = \frac{c_c\text{ __4__}}{\text{ __8__}} = \frac{\text{ __5__ m __6__ ml}}{\text{ __9__ ml}} =$ 7 m
the dilution factor is the ratio of either volumes or concentrations, either $v_c/v_d$ or $c_d/c_c$
the dilution factor is 10
a. $c_d$ b. $c_c$ c. $v_d$ d. $v_c$ e. 10.0 f. 90.0
g. 100.0 h. 5.00 i. 4.00 j. 3.00 k. 2.00 l. 1.00
m. 0.500 n. 1:1 o. 1:2 p. 1:5 q. 1:10 r. 1:100
s. 2:5 t. 1:50 u. 0.400

Explanation:

Step1: Determine the values of \(V_c\), \(V_d\), and \(C_c\)

• \(V_c\) (volume of concentrated solution) is \(10.0\) mL (given as the volume of the initial solution).
• \(V_d\) (volume of diluted solution) is \(10.0 + 90.0=100.0\) mL (sum of the initial solution volume and water volume).
• \(C_c\) (concentration of concentrated solution) is \(5.00\) M (given).

Step2: Use the dilution formula \(C_dV_d = C_cV_c\) to solve for \(C_d\)

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Step3: Calculate the dilution factor

The dilution factor \(=\frac{V_c}{V_d}=\frac{10.0}{100.0}=\frac{1}{10}\) (or \(1:10\))

Answer:

1. \(E\) (10.0)
2. \(G\) (100.0)
3. \(H\) (5.00)
4. \(V_c\) (\(D\))
5. \(H\) (5.00)
6. \(E\) (10.0)
7. \(M\) (0.500)
8. \(V_d\) (\(C\))
9. \(G\) (100.0)
10. \(Q\) (1:10)