Question

molarity masterydiagramming the concept...1. use this diagram 2 m determine the concentration of the following100 ml400ml2. you are given a 3m solution of calcium chloride. you increase the molarity to 6m.explain how you would go about making the change.plugging & chugging...3. what is the concentration of a solution made by dissolving 8.5 grams of calciumchloride in 350. ml of water?4. how many grams of barium nitrate need to dissolved in 600. ml of water in order tomake a 2.3 m solution?5. you need to make a 0.65 m solution of sodium phosphate. if you have 4.3 grams of thethe solid, what volume of solution can you make?

Explanation:

Step1: Apply dilution formula

Use $M_1V_1 = M_2V_2$, solve for $M_2$:
$M_2 = \frac{M_1V_1}{V_2}$
Substitute $M_1=2\ \text{M}$, $V_1=100\ \text{mL}$, $V_2=400\ \text{mL}$:
$M_2 = \frac{2 \times 100}{400}$

Step2: Calculate final concentration

$M_2 = 0.5\ \text{M}$

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Step1: Explain molarity increase logic

Molarity $M=\frac{\text{moles}}{\text{volume}}$. To double $M$, either halve volume (remove solvent) or double moles (add solute).
Practical method: Evaporate solvent from the 3M solution until the volume is reduced to half its original value, or add an equal number of moles of calcium chloride to the original solution while keeping volume constant.

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Step1: Find molar mass of $\text{CaCl}_2$

Molar mass of $\text{Ca}=40.08\ \text{g/mol}$, $\text{Cl}=35.45\ \text{g/mol}$:
$\text{Molar mass} = 40.08 + 2\times35.45 = 110.98\ \text{g/mol}$

Step2: Calculate moles of $\text{CaCl}_2$

$\text{Moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{8.5}{110.98} \approx 0.0766\ \text{mol}$

Step3: Convert volume to liters

$350\ \text{mL} = 0.350\ \text{L}$

Step4: Calculate molarity

$M = \frac{\text{moles}}{\text{volume}} = \frac{0.0766}{0.350} \approx 0.22\ \text{M}$

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Step1: Find molar mass of $\text{Ba(NO}_3\text{)}_2$

Molar mass of $\text{Ba}=137.33\ \text{g/mol}$, $\text{N}=14.01\ \text{g/mol}$, $\text{O}=16.00\ \text{g/mol}$:
$\text{Molar mass} = 137.33 + 2\times(14.01 + 3\times16.00) = 261.35\ \text{g/mol}$

Step2: Calculate moles needed

$M = \frac{\text{moles}}{\text{volume}} \implies \text{moles} = M \times \text{volume}$
Convert $600\ \text{mL}=0.600\ \text{L}$:
$\text{Moles} = 2.3 \times 0.600 = 1.38\ \text{mol}$

Step3: Calculate mass required

$\text{Mass} = \text{moles} \times \text{molar mass} = 1.38 \times 261.35 \approx 360.66\ \text{g}$

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Step1: Find molar mass of $\text{Na}_3\text{PO}_4$

Molar mass of $\text{Na}=22.99\ \text{g/mol}$, $\text{P}=30.97\ \text{g/mol}$, $\text{O}=16.00\ \text{g/mol}$:
$\text{Molar mass} = 3\times22.99 + 30.97 + 4\times16.00 = 163.94\ \text{g/mol}$

Step2: Calculate moles of $\text{Na}_3\text{PO}_4$

$\text{Moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{4.3}{163.94} \approx 0.0262\ \text{mol}$

Step3: Calculate solution volume

$M = \frac{\text{moles}}{\text{volume}} \implies \text{volume} = \frac{\text{moles}}{M}$
$\text{Volume} = \frac{0.0262}{0.65} \approx 0.0403\ \text{L} = 40.3\ \text{mL}$

Answer:

1. $\boldsymbol{0.5\ \text{M}}$
2. Evaporate solvent to reduce the solution's volume to half of its original volume, or add an equal number of moles of calcium chloride to the original 3M solution while maintaining the same total volume.
3. $\boldsymbol{\approx 0.22\ \text{M}}$
4. $\boldsymbol{\approx 361\ \text{g}}$ (rounded to 3 significant figures)
5. $\boldsymbol{\approx 40\ \text{mL}}$ (rounded to 2 significant figures)