Concentration Calculations - Pharmacy Technician Certification Exam Ptce

1. Identify the percent strength (% $w/v$) of a solution labeled $5\ \text{mg/mL}$.

   $0.5\%\ w/v$. 5 mg/mL equals 0.5 g per 100 mL, corresponding to 0.5% w/v.

2. State the dilution equation used to relate initial and final concentrations.

   $C_1V_1 = C_2V_2$. The dilution equation equates the product of concentration and volume before and after dilution.

3. What is the concentration in mg/mL after reconstituting $1\ \text{g}$ to a final volume of $20\ \text{mL}$?

   $50\ \text{mg/mL}$. Concentration after reconstitution is total mg divided by final mL volume.

4. Calculate $V_1$: prepare $100\ \text{mL}$ of $2\ \text{mg/mL}$ from $10\ \text{mg/mL}$ stock.

   $20\ \text{mL}$. The dilution formula $C_1V_1 = C_2V_2$ solves for the initial stock volume needed.

5. What is the formula to convert mg/mL concentration to % $w/v$?

   % $w/v$ = $\frac{\text{mg/mL}}{10}$. Dividing mg/mL by 10 converts to grams per 100 mL, defining percent w/v.

6. What is the equivalence between ppm and mg/L for dilute aqueous solutions?

   $1\ \text{ppm} = 1\ \text{mg/L}$. For dilute aqueous solutions, 1 ppm equates to 1 mg per liter due to water's density approximation.

7. Identify the concentration in mg/mL of a $2\%$ $w/v$ solution.

   $20\ \text{mg/mL}$. A 2% w/v solution contains 2 g per 100 mL, equivalent to 20 mg per mL.

8. Identify the percent strength (% $w/v$) equivalent to ratio strength $1:200$.

   $0.5\%\ w/v$. 1:200 means 1/200 or 0.005, multiplied by 100 yields 0.5% w/v.

9. Calculate $V_2$: dilute $30\ \text{mL}$ of $10\%$ to a final concentration of $2\%$.

   $150\ \text{mL}$. Rearranging $C_1V_1 = C_2V_2$ gives the final volume after dilution.

10. State the formula for ratio strength when expressed as $1:x$ (w/v or v/v).

    Ratio $1:x$ means $1$ unit solute in $x$ units final solution. Ratio strength denotes one part solute diluted to x parts total solution for w/v or v/v expressions.

11. Identify the ratio strength equivalent to $0.02\%$ $w/v$.

    $1:5000$. 0.02% w/v converts to decimal 0.0002, with reciprocal giving the ratio denominator.

12. State the formula for percent strength when a mixture is expressed as % $w/w$.

    % $w/w$ = $\frac{\text{g solute}}{\text{g mixture}}\times 100$. This formula determines the grams of solute per 100 grams of the total mixture for percent weight/weight.

13. State the formula for parts per million (ppm) for dilute aqueous solutions.

    $\text{ppm} = \frac{\text{parts solute}}{10^6\text{ parts solution}}$. Parts per million measures solute parts relative to one million parts of the total solution in dilute cases.

14. What is the formula to convert % $w/v$ to mg/mL concentration?

    $\text{mg/mL} = 10\times$ (% $w/v$). Multiplying percent w/v by 10 yields mg/mL, as 1% w/v equals 10 mg/mL.

15. Calculate final volume after adding $5\ \text{mL}$ drug to $95\ \text{mL}$ diluent.

    $100\ \text{mL}$. Final volume is the sum of the drug and diluent volumes added together.

16. Calculate the final volume needed to obtain $100\ \text{mg/mL}$ from $2\ \text{g}$ of powder.

    $20\ \text{mL}$. Final volume is total mg of powder divided by desired mg/mL concentration.

17. Calculate the amount of drug in mg in $20\ \text{mL}$ of a $25\ \text{mg/mL}$ solution.

    $500\ \text{mg}$. Total drug amount is volume multiplied by concentration in mg/mL.

18. Calculate ppm for $0.01\%$ $w/v$ (assume aqueous solution and $1\% = 10{,}000\ \text{ppm}$).

    $100\ \text{ppm}$. 0.01% w/v multiplied by 10,000 (since 1% = 10,000 ppm) gives 100 ppm.

19. Calculate the final concentration in mg/mL: $500\ \text{mg}$ added to make $250\ \text{mL}$ total volume.

    $2\ \text{mg/mL}$. Final concentration is total mg divided by total mL volume.

20. State the formula for percent strength when a solution is expressed as % $v/v$.

    % $v/v$ = $\frac{\text{mL solute}}{\text{mL solution}}\times 100$. This formula calculates the volume of solute in milliliters per 100 mL of total solution for percent volume/volume.

21. State the formula for percent strength when a solution is expressed as % $w/v$.

    % $w/v$ = $\frac{\text{g solute}}{\text{mL solution}}\times 100$. This formula expresses the weight of solute in grams per 100 mL of solution for percent weight/volume concentration.

22. Calculate mL to withdraw for a $150\ \text{mg}$ dose from a vial labeled $75\ \text{mg/mL}$.

    $2\ \text{mL}$. Volume for the dose is mg required divided by vial concentration.

23. Calculate the amount of solute in grams in $500\ \text{mL}$ of a $5\%$ $w/v$ solution.

    $25\ \text{g}$. 5% w/v means 5 g per 100 mL, so 500 mL requires scaling by 5.

24. What is the concentration in mg/mL of a $0.9\%$ $w/v$ sodium chloride solution?

    $9\ \text{mg/mL}$. 0.9% w/v indicates 0.9 g per 100 mL, or 9 mg per mL.

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