Question

Our task is to measure the volume of blood in a live hippopotamus. One way to do this would be to drain its blood into a suitable container and measure its volume. Aside from the obviously disastrous effect this method would have on the hippo, it would not be very accurate since some blood would still remain behind in the tissues. Instead, we will inject the hippo with \(2.00 \mathrm{~mL}\) of a \(2.00 \mathrm{M}\) dye solution which the hippo will not appreciably metabolize or excrete in one hour, and then measure the dye concentration in the bloodstream after 30 minutes (which should be sufficient time for the dye to thoroughly mix in the bloodstream). After 30 minutes, the concentration of the dye in a \(78.0 \mathrm{~mL}\) blood sample was found to be \(0.0000125 \mathrm{M}\). What is the volume of blood in the hippo?

Short answer

The volume of blood in the live hippopotamus is approximately \(320,000 \mathrm{~mL}\).

Step-by-step solution

Write down the given values

First, let's identify the given values in the problem: \(M_1 = 2.00 \mathrm{M}\) (initial concentration of dye), \(V_1 = 2.00 \mathrm{~mL}\) (volume of dye injected), \(M_2 = 0.0000125 \mathrm{M}\) (concentration of dye after 30 minutes), \(V_2\) = volume of blood in the hippo (unknown).

Use the formula \(M_1V_1 = M_2V_2\)

Now, we will use the formula \(M_1V_1 = M_2V_2\) and substitute the given values into the equation: \(M_1V_1 = M_2V_2\)

Substitute the given values and solve for V2

Now, let's substitute the given values into the equation: \((2.00 \mathrm{M})(2.00 \mathrm{~mL}) = (0.0000125 \mathrm{M})(V_2)\) Now, solve for \(V_2\): \(V_2 = \frac{(2.00 \mathrm{M})(2.00 \mathrm{~mL})}{(0.0000125 \mathrm{M})}\) \(V_2 = \frac{4.00 \mathrm{~mL}}{0.0000125 \mathrm{M}}\) \(V_2 = 320000 \mathrm{~mL}\) The volume of blood in the live hippopotamus is approximately 320,000 mL.

Key concepts

Concentration

Concentration refers to the amount of a substance per defined space, often described in terms of how much of that substance exists within a certain volume of solution. It is a key concept in chemistry, especially when dealing with solutions.

Contributing to concentration measurements, several units are commonly used, including molarity, molality, and parts per million (ppm). In this discussion, we will focus on molarity, which is the most prevalent unit for expressing concentration of solutions in a lab setting.

Understanding concentration is essential for calculating how solutions will interact when mixed or diluted. It is also crucial when determining the volume of blood, as seen in the exercise, where the concentration needed to be determined after mixing to find the total blood volume.

Volume Measurement

Volume measurement is critical in chemistry, especially in solution preparation and reactions. It refers to determining the amount of space a substance occupies, often measured in liters (L) or milliliters (mL).

In the context of our exercise, measuring volume accurately ensures precise calculations, like when determining the volume of blood in a hippopotamus.

Typically, volumetric flasks, pipettes, and burettes are used for precise measurement of liquids. Accurate volume measurement helps avoid errors in chemical calculations, which could result in incorrect solution concentrations or reaction yields.

Molarity

Molarity, represented as \(M\), is a measure of concentration in chemistry, defined as the number of moles of solute per liter of solution. It provides a straightforward way to relate the amount of substance present in a solution to its volume.

The formula for molarity is given by: \[ M = \frac{n}{V} \] where \(n\) is the number of moles of the solute and \(V\) is the volume of the solution in liters.

Molarity plays a vital role in stoichiometry, helping chemists deduce how much of each reactant is needed for a reaction or how a solution will behave during dilution processes. In the hippo exercise, knowing the molarity of both the injected dye and the resulting concentration was essential to calculate the total blood volume accurately.

Chemical Solutions

Chemical solutions are homogeneous mixtures composed of two or more substances. Solutions are thoroughly mixed at the molecular level, making them uniform throughout.

Each solution consists of a solute and a solvent. The solute is the substance being dissolved, while the solvent is the substance that does the dissolving, typically present in a larger amount. Water is the most common solvent in solutions.

Understanding how solutions work is vital in determining how to calculate dilution and concentration changes. For example, in the hippo exercise, the dye acts as a solute, mixed into the blood, which is the solvent, to allow the calculation of the total blood volume based on the change in concentration.