Question

guided practice activity #4 - sedative
your veterinarian is administering a sedative to your 40 pound dog bella. the sedative is mixed in saline solution. unfortunately the solution is pre - mixed at 2.5% for a horse and it needs to be a 0.5% concentration to be administered at 10 ml per pound for your dog. how much saline water needs to be added to the current solution to reduce the concentration to 0.5% and have the correct dosage for bella?

Explanation:

Step1: Calculate the total volume of the new solution needed

The dog weighs 40 pounds and the dosage is 10 ml per pound. So the volume of the new solution \(V_{new}\) is \(V_{new}=40\times10 = 400\) ml.

Step2: Use the formula for concentration \(C_1V_1 = C_2V_2\)

Let the volume of the original solution be \(V_1\). We know \(C_1 = 2.5\%\) (or \(0.025\) in decimal), \(C_2=0.5\%\) (or \(0.005\) in decimal) and \(V_2 = 400\) ml.
From \(C_1V_1=C_2V_2\), we can solve for \(V_1\):

$$V_1=\frac{C_2V_2}{C_1}=\frac{0.005\times400}{0.025}=\frac{2}{0.025}=80$$

ml.

Step3: Calculate the volume of saline water to add

Let \(x\) be the volume of saline water to add. We know \(V_2=V_1 + x\). So \(x = V_2-V_1\).
Substitute \(V_1 = 80\) ml and \(V_2 = 400\) ml, we get \(x=400 - 80=320\) ml.

Answer:

320 ml of saline water needs to be added.