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Essential Math and Calculations for Pharmacy Technicians

Indra K. Reddy, Mansoor A. Khan

Chapter 11

Dealing with Reconstitutions - all with Video Answers

Educators

Chapter Questions

Problem 1

Assuming that the dry powder does not contribute to the final volume, how many milliliters of the reconstituted solution must be used to obtain the $6,000,000 \mathrm{IU}$ of long-acting penicillin from an original concentration of $12,000,000 / 5 \mathrm{~mL}$ ?

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Problem 1

Neomycin sulfate is available in $1 \mathrm{~g}$ vials of maximum volume of $10 \mathrm{~mL}$ and the dry powder accounts for $0.9 \mathrm{~mL}$ of the final volume of the reconstituted product. Using a 1-g vial of neomycin sulfate and sterile water for injection as a diluent, how would you obtain the antibiotic concentration needed for the following prescription?
$\mathrm{R}$
Neomycin sulfate $\quad 500 \mathrm{mg}$
Water for injection ad $30 \mathrm{~mL}$
Sig. For topical use only.

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Problem 1

A leaflet enclosed with a vial containing $6,000,000$ units of penicillin G sodium states, "When $30 \mathrm{~mL}$ of sterile diluent are added the dry powder resulting concentration is 250,000 units $/ \mathrm{mL}$." Based on this information, how many milliliters of sterile water for injection should be used in preparing the following prescription?
$\mathrm{R}$
Penicillin G potassium 6000,000 units
Water for injection ad Q.S.
Prepare a solution to contain 600,000 units $/ \mathrm{mL}$
Sig. $1 \mathrm{~mL}=600,000$ units of penicillin $\mathrm{G}$ sodium

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Problem 2

Assuming that the dry powder does not contribute to the final volume, how many milliliters of the reconstituted solution must be used to obtain the $3,000,000 \mathrm{IU}$ of long-acting penicillin from an original concentration of $12,000,000 / 4 \mathrm{~mL}$ ?

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Problem 3

A pharmacist receives a medication order for 600,000 units of penicillin G sodium to be added to one liter of D5W. A vial of penicillin G sodium containing a million units is on hand, and the directions on this vial state, "Add 5 milliliters of sterilized water for $2 \times 10^5$ units $/ \mathrm{mL}$ ". How many milliliters of the reconstituted solution must be added to the D5W to provide the desired concentration?

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Problem 4

A pharmacist receives a medication order to prepare different concentrations of penicillin $\mathrm{G}$ potassium to be added to $1000 \mathrm{~mL}$ of D5W, using stock vials of $1,000,000$ units of penicillin G sodium. The instructions on the vials of penicillin G potassium stated, "Add 4.6 milliliters of sterilized water for a concentration of $2.5 \times 10^5$ units $/ \mathrm{mL}$." How many milliliters of the reconstituted solution must be added to the D5W to provide the following units of penicillin G sodium in the final preparation?
a. $2 \times 10^5$ units
b. $4 \times 10^5$ units
c. $5 \times 10^5$ units
d. $6 \times 10^5$ units
e. $2 \times 10^6$ units
f. $1 \times 10^6$ units

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Problem 5

Using a vial containing 300,000 units of penicillin $G$ potassium, how many milliliters of sterile water for injection should be added to the dry powder in preparing a solution having a concentration of 30,000 units $/ \mathrm{mL}$ ?

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Problem 6

Using a vial containing 300,000 units of penicillin G sodium, how many milliliters should be added to the dry powder in preparing a solution having a concentration of 25,000 units $/ \mathrm{mL}$ ?

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Problem 7

Using a vial containing 12 million units of long-acting penicillin, how many milliliters of sterile water for injection should be added to the dry powder in preparing a solution having concentration of $2,000,000$ units $/ \mathrm{mL}$ ?

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Problem 8

Using a vial containing $1,000,000$ units of penicillin G sodium, how many milliliters of diluent should be added to the dry powder in preparing a solution having a concentration of 250,000 units $/ \mathrm{mL}$ ?

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Problem 9

Assuming that the dry powder does not contribute to the final volume, how many milliliters of the reconstituted solution must be used to obtain $300,000 \mathrm{IU}$ of penicillin $\mathrm{G}$ potassium from original concentration of $1,000,000 / 2 \mathrm{~mL}$ ?

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Problem 10

Using a vial of $5,000,000$ units of penicillin $\mathrm{G}$ sodium and normal saline as diluent, how would you obtain the required units of penicillin $\mathrm{G}$ sodium to compound the following prescription?
$\mathrm{R}$
Penicillin G sodium $\quad 40,000$ units/ $\mathrm{mL}$
Normal saline ad $\quad 10 \mathrm{~mL}$
Sig. For IV injection.

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Problem 11

Using a vial of $5,000,000$ units of penicillin G potassium and normal saline as diluent, how would you obtain the required units of penicillin $\mathrm{G}$ sodium to compound the following prescription?
$\mathrm{R}$.
Penicillin G potassium $\quad 10,000$ units $/ \mathrm{mL}$
Normal saline ad $\quad 25 \mathrm{~mL}$
Sig. For topical use.

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Problem 12

Using a vial of $6,000,000$ units of long-acting penicillin and sodium chloride as diluent, how would you obtain the required units of penicillin $\mathrm{G}$ sodium to compound the following prescription?
$\mathrm{R}$.
Long-acting penicillin $200,000 \mathrm{units} / \mathrm{mL}$
Sodium chloride ad $\quad 25 \mathrm{~mL}$
Sig. For topical use.

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Problem 13

Using a vial of $12,000,000$ units of long-acting penicillin and sodium chloride as diluent, how would you obtain the required units of penicillin $\mathrm{G}$ sodium to compound the following prescription?
$\mathrm{R}$.
Long-acting penicillin 400,000 units $/ \mathrm{mL}$
Sodium chloride ad $\quad 20 \mathrm{~mL}$
Sig. For topical use.

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Problem 14

Using a vial containing 450,000 units of penicillin G potassium and sterile water for injection as a diluent, how would you prepare the following prescription?
$\mathrm{R}$
Long-acting penicillin 400,000 units/mL
Sodium chloride ad $\quad 20 \mathrm{~mL}$
Sig. For topical use.

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Problem 15

Using a vial of $6,000,000$ long-acting penicillin and water for injection as a diluent, how would you prepare the following prescription?
$\mathrm{R}$
Long-acting penicillin
Water for injection ad
Sig. For IM injection
$60,000 \mathrm{units} / \mathrm{mL}$
$2 \mathrm{~mL}$

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Problem 16

Using a vial containing 800,000 units of penicillin $\mathrm{G}$ potassium and sterile water for injection as a diluent, how would you prepare the following prescription?
$\mathrm{R}$
Penicillin G potassium 40,000 units/ $\mathrm{mL}$
Water for injection ad $5 \mathrm{~mL}$
Sig. For IM injection

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Problem 19

The antibiotic streptomycin sulfate is in $5 \mathrm{~g}$ vial of $20 \mathrm{~mL}$ maximum capacity, for veterinary use, and the dry powder accounts for $5 \%$ increase of the final volume of reconstituted solution. Using a 5-g streptomycin sulfate vial and water for injection as a diluent, how would you obtain the antibiotic needed for the following prescription?
$\mathrm{R}$
Streptomycin sulfate $1 \mathrm{~g}$
Sodium chloride ad $\quad 100 \mathrm{~mL}$
Sig. For topical use only.

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Problem 20

The information on the leaflets enclosed with a vial containing $5,000,000$ units of penicillin $\mathrm{G}$ sodium states that when $23 \mathrm{~mL}$ saline diluent are added to the dry powder, the resulting concentration is 200,000 units $/ \mathrm{mL}$. Based on this information, how many milliliters of saline should be used in compounding $1,000,000$ units of penicillin G sodium?

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Problem 21

Using the contents of $5 \mathrm{~mL}$ vial of $1-\mathrm{g}$ neomycin sulfate and sterile saline solution as a diluent, how would you obtain the neomycin sulfate required for the following prescription?
$$
\begin{aligned}
& \text { R. } \\
& \text { Neomycin sulfate } \quad 400 \mathrm{mg} \\
& \text { Sodium chloride ad } \quad 20 \mathrm{~mL} \\
& \text { Sig. Use as topical disinfectant. }
\end{aligned}
$$

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Problem 22

A medication order calls for $600 \mathrm{mg}$ of amoxicillin trihydrate to be administered IM to a pneumonic patient every 8 hours. Vials containing $250 \mathrm{mg}, 500 \mathrm{mg}$, and $1 \mathrm{~g}$ of amoxicillin trihydrate are available. Based on the manufacturer's instructions, dilution may made as follows:
$$
\begin{array}{ccc}
\hline \text { Drug Content/Vial } & \text { Volume of Diluent }(\mathrm{mL}) & \text { Final Volume } \\
& & \\
1 / \mathrm{g} & 2 & 2.1 \\
1 / 2 \mathrm{~g} & 5 & 5.2 \\
1 \mathrm{~g} & 10 & 10.5
\end{array}
$$
How could the prescribed dose of the antibiotic be obtained from each of the above three different potencies?

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03:24

Problem 23

A medication order calls for $800 \mathrm{mg}$ of Velosef to be administered IM to a pneumonic patient every 8 hours. Vials containing $250 \mathrm{mg}, 500 \mathrm{mg}$, and $1 \mathrm{~g}$ of Velosef are available. On the basis of manufacturer's instructions, dilution may made as follows:
$$
\begin{array}{ccc}
\hline \text { Drug Content/Vial } & \text { Volume of Diluent }(\mathrm{mL}) & \text { Final Volume } \\
1 / 4 \mathrm{~g} & 2 & 2 \\
1 / 2 \mathrm{~g} & 5 & 5 \\
1 \mathrm{~g} & 10 & 10 \\
\hline
\end{array}
$$
How could the prescribed dose of the antibiotic be obtained from the above three different potencies?

John Barone
John Barone
Numerade Educator

Problem 24

A medication order calls for $300 \mathrm{mg}$ of Cephalexine to be administered IM to a pneumonic patient every 8 hours. Vials containing $500 \mathrm{mg}$, and $1 \mathrm{~g}$ of Cephalexine are available. Dilution may be made according to manufacturer's instructions as follows:

$$
\begin{array}{ccc}
\hline \text { Drug Content/Vial } & \text { Volume of Diluent }(\mathrm{mL}) & \text { Final Volume } \\
1 / 2 \mathrm{~g} & 5 & 5.2 \\
1 \mathrm{~g} & 10 & 10 \\
\hline
\end{array}
$$

How could the prescribed dose of the antibiotic be obtained from the above potencies?

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Problem 25

Using the contents of a $5 \mathrm{~mL}$ vial of $1-\mathrm{g}$ neomycin sulfate and sterile saline solution as a diluent, how would you obtain the neomycin sulfate required for the following prescription?
$\mathrm{R}_{\mathrm{x}}$
Neomycin sulfate $\quad 500 \mathrm{mg}$
Sodium chloride ad $\quad 20 \mathrm{~mL}$
Sig. Use as topical disinfectant.

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Problem 26

Using the contents of a 1,000,000-unit vial polymyxin B sulfate and sterile saline solution as a diluent, how would you obtain the antibiotic required to compound the following prescription?
$\mathrm{R}$
Polymyxin B sulfate $\quad 200,000$ units $/ \mathrm{mL}$
Sodium chloride ad $\quad 30 \mathrm{~mL}$
Sig. Use as topical disinfectant.

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Problem 27

A medication order calls for $1 \mathrm{~g}$ of amoxicillin monohydrate and sterile water for injection as a diluent, how would you obtain amoxicillin monohydrate needed to prepare the following prescription?
$\mathrm{R}$
Amoxicillin monohydrate $500 \mathrm{mg}$
Sodium chloride ad $\quad 15 \mathrm{~mL}$
Sig. Infantile suspension.
15 drops to be taken orally every $8 \mathrm{hr}$.

Gayathri Janakiraman Paramasivan
Gayathri Janakiraman Paramasivan
Numerade Educator
03:24

Problem 28

Using a vial of $600 \mathrm{mg}$ Velosef, how many milliliters of sterile water for injection should be added to the dry Velosef powder for preparing a solution having $150 \mathrm{mg} / \mathrm{mL}$ of the antibiotic Velosef?

John Barone
John Barone
Numerade Educator

Problem 29

Using a vial containing $750 \mathrm{mg}$ of amoxicillin monohydrate, how many milliliters of water for injection should be added to the dry powder to prepare a solution having a concentration of $500 \mathrm{mg} / \mathrm{mL}$ of amoxicillin monohydrate? Assume that the dry powder does not contribute to the final volume.

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Problem 30

For preparation of Augmentin (amoxicillin trihydrate and clavulanic acid as a potassium salt) oral suspension, 5 grams of the dry powder should be diluted with $45 \mathrm{~mL}$ of sterile water for injection to obtain a final solution containing $312 \mathrm{mg} / \mathrm{mL}$. If the ratio between amoxicillin trihydrate and clavulanic acid as a potassium salt is $4: 1$, how much of each drug is present in $9 \mathrm{~mL}$ of suspension?

Gayathri Janakiraman Paramasivan
Gayathri Janakiraman Paramasivan
Numerade Educator

Problem 31

A medication order calls for $300 \mathrm{mg}$ of Cefazolin sodium to be administered IM for a patient every 8 hours. Vials containing $250 \mathrm{mg}$ and $500 \mathrm{mg}$ are available. Based on the enclosed pamphlet's instructions, dilution can be made as follows:

$$
\begin{array}{ccc}
\hline \text { Drug Content/Vial } & \text { Volume of Diluent }(\mathrm{mL}) & \text { Final Volume } \\
1 / 4 \mathrm{~g} & 2 & 2.1 \\
1 / 2 \mathrm{~g} & 2 & 2.2 \\
\hline
\end{array}
$$

How could the prescribed dose of the antibiotic be obtained from the above strengths?

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01:26

Problem 32

A new hepatitis A vaccine offers a reduction in the number of doses to be taken. For this vaccine, vials containing 360 and 720 Enzyme-Linked Immunosorbent Assay (ELISA) units are available. According to the manufacturer's instructions, dilution may be made as follows:

$$
\begin{array}{ccc}
\hline \text { No. of Units/Vial } & \text { Volume of Diluent }(\mathrm{mL}) & \text { Final Volume } \\
360 & 1 & 1.05 \\
720 & 1 & 1.1 \\
\hline
\end{array}
$$

Based on the above information, how could a prescribed dose of $400 \mathrm{EL}-\mathrm{U}$ be obtained from the above strengths?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
00:49

Problem 33

A new hepatitis A vaccine offers fewer doses to be taken. For this vaccine, vials containing 360 and $720 \mathrm{EL}-\mathrm{U}$ are available. According to the manufacturer's instructions, dilution may be made as follows:

$$
\begin{array}{ccc}
\hline \text { No. of Units/Vial } & \text { Volume of Diluent }(\mathrm{mL}) & \text { Final Volume } \\
360 & 1 & 1.05 \\
720 & 1 & 1.1 \\
\hline
\end{array}
$$

Liuxi Sun
Liuxi Sun
Numerade Educator

Problem 34

For a new hepatitis A vaccine that offers fewer doses to be taken, vials containing $1440 \mathrm{EL}-\mathrm{U}$ are available. According to the manufacturer's instructions, the dose will be ready after adding $2 \mathrm{~mL}$ of the diluent to the dry lyophilized powder. The final volume is expected to be $10 \%$ more upon reconstitution. Based on this information, how can the following doses be obtained?
a. $1000 \mathrm{EL}-\mathrm{U}$
b. $1500 \mathrm{EL}-\mathrm{U}$
c. $850 \mathrm{EL}-\mathrm{U}$
d. $1250 \mathrm{EL}-\mathrm{U}$

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Problem 35

According to the package insert enclosed with a penicillin G potassium vial, the reconstituted solution is prepared by dissolving 250,000 units and the dry powder accounts for $1 \mathrm{~mL}$ increase in the final volume. Based on this information, how would you obtain the antibiotic required to compound the following prescription?
\begin{tabular}{ll}
R. & \\
Penicillin G potassium & 250,000 units \\
Diluent ad & Q.S. \\
Make solution containing 25,000 units $/ \mathrm{mL}$
\end{tabular}

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Problem 36

A pharmacist has received a medication order for 100,000 units of penicillin $\mathrm{G}$ sodium to be added to $250 \mathrm{~mL}$ of D5W. A vial of penicillin G sodium containing one million units is on hand and the direction on the vial states, "Add $44.8 \mathrm{~mL}$ of sterile water for injection to obtain a concentration of 200,000 units $/ \mathrm{mL}$." How many milliliters of the reconstituted solution should be withdrawn and added to the D5W?

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