Question

how many l of a 5.00 m solution are needed to make 2.00 l of a 1.00 m 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_d =$1 l $v_c = ? c_c =$2 m $c_d =$3 m
solving for $v_c$ first put in the symbols, then put in the numbers
$v_c = \frac{v_d\text{__4__}}{\text{__8__}} = \frac{\text{__5__ l __6__ m}}{\text{__9__ m}} =$7 l
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: Identify the variables

The dilution equation is \(C_dV_d = C_cV_c\). Here, \(V_d = 2.00\) L (the volume of the diluted solution), \(C_d=1.00\) M (the concentration of the diluted solution), \(C_c = 5.00\) M (the concentration of the concentrated solution), and \(V_c\) (the volume of the concentrated solution) is the unknown.

Step2: Rearrange the formula to solve for \(V_c\)

From \(C_dV_d = C_cV_c\), we can get \(V_c=\frac{C_dV_d}{C_c}\).

Step3: Substitute the values

Substitute \(C_d = 1.00\) M, \(V_d=2.00\) L, and \(C_c = 5.00\) M into the formula: \(V_c=\frac{1.00\space M\times2.00\space L}{5.00\space M}\).

Step4: Calculate the value

\(V_c=\frac{2.00}{5.00}= 0.400\) L.

For the dilution factor, using the formula \(DF=\frac{C_d}{C_c}\) (or \(\frac{V_c}{V_d}\)), substituting \(C_d = 1.00\) M and \(C_c = 5.00\) M, we get \(DF=\frac{1.00}{5.00}=\frac{1}{5}\) (or using \(V_c = 0.400\) L and \(V_d=2.00\) L, \(DF=\frac{0.400}{2.00}=\frac{1}{5}\)).

Answer:

1. \(K\) (since \(V_d = 2.00\) L)
2. \(L\) (since \(C_d=1.00\) M)
3. \(H\) (since \(C_c = 5.00\) M)
4. \(A\) (because we use \(C_d\) in the formula \(V_c=\frac{C_dV_d}{C_c}\))
5. \(K\) (\(V_d = 2.00\) L)
6. \(L\) (\(C_d = 1.00\) M)
7. \(U\) (\(V_c=0.400\) L)
8. \(B\) (because we divide by \(C_c\) in the formula \(V_c=\frac{C_dV_d}{C_c}\))
9. \(H\) (\(C_c = 5.00\) M)
10. \(P\) (dilution factor \(\frac{C_d}{C_c}=\frac{1}{5}\) or \(1:5\))