Question

a childrens cough syrup contains 25.0 mg of benzocaine (a numbing agent) per 5.00 milliliters of syrup. the bottle instructs a parent to give a max of 5.00 mg per kilogram of body weight per day. how many ml of the cough syrup can a 32.0 lb toddler take in one day? 1 lb = 0.453 kg
72.6 ml
83.2 ml
32.0 ml
14.5 ml
question 24
1 pts
solve the following equation for the volume: pv = nrt
v = nrt/p
v = nrt×p
v = nr/tp
v = p/nrt

Explanation:

Question 1

Step1: Convert weight from lb to kg

Given $1\ lb = 0.453\ kg$, for a $32.0\ lb$ toddler, the weight in kg is $m = 32.0\times0.453\ kg=14.496\ kg$.

Step2: Calculate the maximum amount of Benzocaine

The maximum dose is $5.00\ mg$ per kg of body - weight per day. So the maximum amount of Benzocaine for the toddler is $M = 5.00\ mg/kg\times14.496\ kg = 72.48\ mg$.

Step3: Calculate the volume of cough - syrup

The cough - syrup contains $25.0\ mg$ of Benzocaine per $5.00\ mL$. Let the volume of the cough - syrup be $V$. We have the proportion $\frac{25.0\ mg}{5.00\ mL}=\frac{72.48\ mg}{V}$. Solving for $V$, we get $V=\frac{72.48\ mg\times5.00\ mL}{25.0\ mg}=14.496\ mL\approx14.5\ mL$.

We are given the ideal gas law $PV = nRT$. To solve for the volume $V$, we need to isolate $V$ on one side of the equation. Divide both sides of the equation $PV=nRT$ by $P$ (assuming $P
eq0$). So $V=\frac{nRT}{P}$.

Answer:

14.5 mL

Question 2