Question

What is the molarity of a solution that contains \(50.0 \mathrm{~g}\) of vitamin \(\mathrm{B}_{1}\) hydrochloride (molar mass \(=337 \mathrm{~g} / \mathrm{mol}\) ) in \(160 \mathrm{~mL}\) of solution?

Short answer

The molarity of the solution is approximately 0.927 M.

Step-by-step solution

Calculate moles of Vitamin B1 Hydrochloride

To find the moles of vitamin B1 hydrochloride, use the formula \( ext{moles} = \frac{\text{mass}}{\text{molar mass}} \). Here, the mass is \(50.0 \text{ g}\) and the molar mass is \(337 \text{ g/mol}\). Thus, moles = \( \frac{50.0}{337} \approx 0.1483 \text{ moles} \).

Convert the Volume to Liters

Molarity is expressed in terms of liters of solution, so we must convert \(160 \text{ mL}\) to liters. \(160 \text{ mL} = 0.160 \text{ L}\) since \(1 \text{ L} = 1000 \text{ mL}\).

Calculate the Molarity

Molarity is defined as the number of moles of solute per liter of solution, so use the formula \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \). Taking the moles from Step 1 as \(0.1483 \text{ moles}\) and the volume from Step 2 as \(0.160 \text{ liters}\), the molarity is \( \frac{0.1483}{0.160} \approx 0.927 \text{ M}\).

Key concepts

Vitamin B1 Hydrochloride

Vitamin B1 Hydrochloride, also known as thiamine hydrochloride, is a water-soluble vitamin critical for maintaining proper body function. It plays a key role in energy metabolism, helping to convert nutrients into energy. Because it's water-soluble, our bodies do not store it, leading to the necessity for regular intake through diet or supplements.
In chemical calculations, Vitamin B1 Hydrochloride is often encountered in molarity problems due to its defined molecular composition. Knowing its chemical behavior helps in understanding how it interacts in solutions. By measuring its concentration in a solution, we can address various biological and chemical queries related to its activity in the body.

Molar Mass

Molar mass is a fundamental concept in chemistry important for converting between grams and moles. It is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol).
For Vitamin B1 Hydrochloride, the molar mass is given as 337 g/mol. This value is calculated by adding up the atomic masses of each constituent atom in the compound. Understanding the molar mass allows you to determine how much of the substance you have in terms of moles, which is crucial when calculating concentrations like molarity.

Solution Volume

Solution volume is a key component in calculating molarity, representing the total space a solution occupies. Volumes in calculations are typically expressed in liters.
In our example, the solution volume is initially provided in milliliters (mL). To convert milliliters to liters, remember that 1 liter equals 1000 milliliters. This conversion is essential because molarity is defined as moles per liter. Hence, for a solution volume of 160 mL, it becomes 0.160 L in the molarity formula. Understanding and converting solution volume accurately ensures precise chemical calculations.

Chemical Calculations

Chemical calculations form the basis of predicting the outcomes in many chemical reactions and conditions. Molarity, an important aspect of these calculations, measures the concentration of a solute in a solution. It's calculated using the formula \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \).
To find molarity, first calculate the moles of solute using its mass and molar mass. Then convert the solution volume to liters. Using these figures, apply the formula to determine the molarity. Such calculations are crucial for experiments, reactions, and understanding the properties of solutions.