Chapter 3, Problem 3.31P

Interpretation Introduction

(a)

Interpretation:

The volume of the API in mL to be sprayed for the patients with specified mass is to be calculated. Also, number of drops in every prescribed dose of the drug is to be calculated.

Concept introduction:

Mass of the drug $\left(m_{\text{d}}\right)$ required for the given mass of patient $\left(m_{\text{P}}\right)$ and the prescribed dose $\left(D\right)$ is:

$m_{\text{d}}=m_{\text{P}}\times D$   ........ (1)

Number of moles $\left(n\right)$ is calculated by the formula:

$n=\frac{m}{\text{MW}}$   ........ (2)

Here, $m$ is the mass of the substance in $\text{'}\text{g}\text{'}$ and $\text{MW}$ is the molecular mass of the substance in $\text{'}\text{g/mol}\text{'}$.

Molarity $\left(M\right)$ of any solution is calculated as:

$M=\frac{n}{V}$   ........ (3)

Here, $V$ is the volume of the solution in $\text{'}\text{L}\text{'}$.

Number of drops $\left(N_{\text{d}}\right)$ is calculated as:

$N_{\text{d}}=\frac{V}{V_{\text{d}}}$   ........ (4)

Here, $V$ is the volume of the solution in $\text{'}\text{mL}\text{'}$ and $V_{\text{d}}$ is the volume of one drop of the solution in $\text{'}\text{mL}\text{'}$.

Volume of a sphere $\left(V_s\right)$ is given by:

$V_s=\frac{4}{3}\pi r^3$   ........ (5)

Here, $r$ is the radius of the sphere in $\text{'}\text{m}\text{'}$.

Interpretation Introduction

(b)

Interpretation:

The formula for the volume, $V_{\text{dose}}\left(\text{mL}\right)$ in terms of the specified variables is to be derived. Also, the derived formula is to be checked for the values given in part (a).

Concept introduction:

Weight $\left(W\right)$ in $\text{'}\text{N}\text{'}$ of an object is calculated as:

$W=m\times \text{g}$   ........ (6)

Here, $m$ is the mass of that object in $\text{'}\text{kg}\text{'}$ and $\text{g}$ is the acceleration due to gravity, $\text{g}=9.8{\text{ m/s}}^2$.

Mass of the drug $\left(m_{\text{d}}\right)$ required for the given mass of patient $\left(m_{\text{P}}\right)$ and the prescribed dose $\left(D\right)$ is:

$m_{\text{d}}=m_{\text{P}}\times D$   ........ (7)

Number of moles $\left(n\right)$ is calculated by the formula:

$n=\frac{m}{\text{MW}}$   ........ (8)

Here, $m$ is the mass of the substance in $\text{'}\text{g}\text{'}$ and $\text{MW}$ is the molecular mass of the substance in $\text{'}\text{g/mol}\text{'}$.

Molarity $\left(M\right)$ of any solution is calculated as:

$M=\frac{n}{V}$   ........ (9)

Here, $V$ is the volume of the solution in $\text{'}\text{L}\text{'}$.

Interpretation Introduction

(c)

Interpretation:

For a sphere of radius ‘r’, its surface-to-volume ratio is to be calculated. Also, the surface area of the sphere for the specified volume and radius is to be determined.

Concept introduction:

Volume of a sphere $\left(V_s\right)$ is given by:

$V_s=\frac{4}{3}\pi r^3$   ........ (11)

Here, $r$ is the radius of the sphere in $\text{'}\text{m}\text{'}$.

Surface area of a sphere $\left(S{A}_s\right)$ is given by:

$S{A}_s=4\pi r^2$   ........ (12)

Here, $r$ is the radius of the sphere in $\text{'}\text{m}\text{'}$.