Question

1. how many ml of 3.00 m nacl solution are needed to make 4.00 l of a 2.00 m solution?

identify the variables ( c_d = 2.00 m ) ( c_c = 3.00 m )
( v_d = 4.00 l ) ( v_c = ? l )
first put in the symbols, then put in the numbers
( v_c=\frac{c_d 1}{c_c}=\frac{(2.00 m)(2 l)}{3.00 m}=3 l )
(4 ml)
((5 l)(\frac{________}{1 l})=6__ ml)

1. what is the dilution factor? first put in the symbols, then put in the numbers

dilution (=\frac{c_d}{8}=\frac{2.00 m}{9 m}=7)
a. 3.000 b. 2.500 c. 10.00 d. 1 e. 2.000
f. 9.000 g. 6.000 h. 8.000 i. 0.02500 j. 47.00
k. 5.00 l. 50.00 m. 25.0 n. 0.02041 o. 97.98
p. 30.62 q. 6.572 r. 0.06124 s. 262.87 t. 0.1800
u. ( 3.000\times10^3 ) v. 7.500 w. 0.6667 x. 0.200 y. 2.67
z. ( 2.67\times10^3 ) aa. ( 10^3 ) bb. ( 10^{-3} ) cc. ( c_c ) dd. ( c_d )

Explanation:

Step1: Use the dilution formula

The dilution formula is \(C_{C}V_{C}=C_{D}V_{D}\), so \(V_{C}=\frac{C_{D}V_{D}}{C_{C}}\).

Step2: Substitute the values

Substitute \(C_{D} = 2.00\space M\), \(V_{D}=4.00\space L\), and \(C_{C}=3.00\space M\) into the formula: \(V_{C}=\frac{(2.00\space M)(4.00\space L)}{3.00\space M}\).

Step3: Calculate \(V_{C}\)

\(V_{C}=\frac{8.00}{3.00}\space L = 2.67\space L\).

Step4: Convert liters to milliliters

Since \(1\space L = 1000\space mL\), then \(V_{C}=(2.67\space L)\times\frac{1000\space mL}{1\space L}=2670\space mL = 2.67\times10^{3}\space mL\).

Step5: Calculate the dilution factor

The dilution factor formula is \(\text{dilution factor}=\frac{C_{C}}{C_{D}}\). Substitute \(C_{D} = 2.00\space M\) and \(C_{C}=3.00\space M\) into the formula: \(\text{dilution factor}=\frac{3.00\space M}{2.00\space M}=1.5\) (This part seems to have some confusion in the original problem setup as the provided options might have a typo. But if we follow the formula \(C_{C}V_{C}=C_{D}V_{D}\), another way for dilution factor is \(\frac{V_{D}}{V_{C}}\), \(\frac{4.00\space L}{2.67\space L}\approx1.5\). But if we consider the formula written as \(\text{dilution}=\frac{C_{D}}{C_{C}}\) (which is actually the reciprocal of the common dilution factor formula), \(\frac{2.00\space M}{3.00\space M}=0.6667\) which is option W.

Answer:

1. \(V_{C} = 2.67\times 10^{3}\space mL\) (corresponds to \(V_{C}\) calculation).
2. If using \(\text{dilution}=\frac{C_{D}}{C_{C}}\), the answer is W. \(0.6667\).