Question

question 6
0.67 pts
you have an injectable calcium solution that is 30 mg/ml. how much do you add to 1 liter of lactated ringers solution to deliver 4 mg/h calcium at a fluid rate of 30 ml/h?

Explanation:

Step1: Determine the concentration - to - rate relationship

Let $x$ be the volume (in ml) of the calcium solution to add. The amount of calcium per hour is related to the concentration of the calcium solution. The concentration of the calcium solution is 30 mg/ml. We want to deliver 4 mg/h of calcium.

Step2: Set up the proportion equation

We know that the amount of calcium per hour is given by the product of the concentration of the calcium solution and the volume of the calcium - containing solution delivered per hour. Since the fluid rate is 30 ml/h, and the concentration of the calcium solution is 30 mg/ml, we have the equation $30x=4\times1000$ (we can also set up a proportion based on the rate. The ratio of calcium amount to volume in the concentrated solution should be the same as the ratio in the final mixture. But a simpler way is to consider the amount of calcium per hour). In terms of the rate, if we consider the amount of calcium per unit volume, we know that in the concentrated solution, there are 30 mg/ml of calcium. We want to have 4 mg of calcium in 30 ml of the final mixture. Let the volume of the concentrated calcium solution be $x$ ml. The amount of calcium in $x$ ml of the 30 mg/ml solution is the same as the amount of calcium we want to deliver per hour. So, from the formula $C_1V_1 = C_2V_2$ (where $C_1$ is the concentration of the concentrated calcium solution, $V_1$ is the volume of the concentrated calcium solution, $C_2$ is the desired calcium concentration in the final mixture, and $V_2$ is the volume of the final mixture per hour), we have $30x=4\times30$.

Step3: Solve the equation for $x$

Divide both sides of the equation $30x = 4\times30$ by 30.
$x=\frac{4\times30}{30}=4$ ml.

Answer:

4 ml