In 2014, a major chemical leak at a facility in West Virginia released 28,390 L of MCHM (4-methylcyclohexylmethanol, C8H16O) into the Elk River. The density of MCHM is 0.9074 g/mL. (a) Calculate the initial molarity of MCHM in the river, assuming that the first part of the river is 2.00 m deep, 90.0 m wide, and 90.0 m long.

Verified step by step guidance

1. Calculate the mass of MCHM using its volume and density. Use the formula: \( \text{mass} = \text{volume} \times \text{density} \). Convert the volume from liters to milliliters first.
2. Convert the mass of MCHM from grams to moles using its molar mass. The molar mass of MCHM (C8H16O) can be calculated by adding the atomic masses of its constituent atoms.
3. Calculate the volume of the first part of the river in liters. Use the formula: \( \text{volume} = \text{depth} \times \text{width} \times \text{length} \). Convert the volume from cubic meters to liters.
4. Determine the initial molarity of MCHM in the river by dividing the number of moles of MCHM by the volume of the river in liters. Use the formula: \( \text{molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \).
5. Ensure all units are consistent throughout the calculations, and check each step for accuracy.

Key Concepts

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L) and is crucial for understanding how much of a substance is present in a given volume of solution. To calculate molarity, one must know both the amount of solute and the total volume of the solution.

Density

Density is the mass per unit volume of a substance, typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). In this context, the density of MCHM allows us to convert the volume of the chemical (in liters) into mass (in grams), which is necessary for calculating the number of moles of the solute.

Volume of the River

The volume of the river section is calculated using its dimensions: depth, width, and length. This volume, expressed in cubic meters or liters, is essential for determining the total amount of water that will dilute the MCHM. Understanding the volume helps in accurately calculating the molarity of the solute in the river water.