Problem 120 - Chemistry Matter and Change

Question

What is the molarity of a solution made by dissolving 25.0 g of sodium thiocyanate (NaSCN) in enough water to make 500 mL of solution? (Chapter 14)

Step-by-Step Solution

Answer

The molarity of the solution is approximately 0.617 M.

Step 1: Calculate Molar Mass of NaSCN

The molar mass of sodium thiocyanate (NaSCN) is calculated by adding the atomic masses of its constituent elements: Na, S, C, and N.- Na: 22.99 g/mol- S: 32.07 g/mol- C: 12.01 g/mol- N: 14.01 g/molSo, the molar mass is \[ 22.99 + 32.07 + 12.01 + 14.01 = 81.08 ext{ g/mol} \]

Step 2: Calculate Moles of NaSCN

To find the number of moles of NaSCN, use the formula:\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]Plugging in the values:\[ \text{moles} = \frac{25.0 \, \text{g}}{81.08 \, \text{g/mol}} \approx 0.3085 \, \text{mol} \]

Step 3: Convert Volume to Liters

The solution volume must be converted from milliliters to liters, as molarity is expressed in moles per liter. Since 500 mL is equivalent to 0.500 L,\[ \text{Volume} = 0.500 \, \text{L} \]

Step 4: Calculate Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. Use the formula:\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \]Plugging in the values:\[ \text{Molarity} = \frac{0.3085 \, \text{mol}}{0.500 \, \text{L}} \approx 0.617 \, \text{M} \]

Key Concepts

Molar Mass Calculation

To determine the molar mass of a compound, you need to sum the atomic masses of all the elements present in the compound. The atomic masses can typically be found on the periodic table. In the case of sodium thiocyanate (NaSCN), you should look at the masses for sodium (Na), sulfur (S), carbon (C), and nitrogen (N). Here's how it adds up:

• Sodium (Na): 22.99 g/mol
• Sulfur (S): 32.07 g/mol
• Carbon (C): 12.01 g/mol
• Nitrogen (N): 14.01 g/mol

Adding these values together gives us:\[ 22.99 + 32.07 + 12.01 + 14.01 = 81.08 \, \text{g/mol} \]Thus, the molar mass of NaSCN is 81.08 g/mol. This value is essential as a foundational step in converting grams of a substance into moles, aiding in further calculations such as molarity.

Sodium Thiocyanate

Sodium thiocyanate, represented by the chemical formula NaSCN, is a white crystalline compound. It is one of the many sodium compounds used in various applications due to its solubility in water and other properties. This compound plays significant roles in different scientific and industrial fields:

• Chemical Reactions: Used as a precursor or reactant in certain chemical syntheses.
• Photography: Employed in the photographic and dye industries due to its ability to stabilize silver thiosulfate complexes.
• Biological Studies: Used in biochemistry and biology labs for testing and as a reagent.

Understanding sodium thiocyanate is crucial in chemistry, especially when discussing solutions and molarity, as it helps provide context to calculations involving its use.

Volume Conversion

When calculating molarity, it is critical to convert the volume of your solution into liters. Molarity is defined as the number of moles of a solute per liter of solution. Often, laboratory measurements might provide volume in milliliters, necessitating a conversion:
A helpful rule to remember is:

• 1 Liter = 1000 milliliters

Therefore, to convert milliliters to liters, divide the number of milliliters by 1000. For example, if you have 500 mL of solution, convert it like this:\[ \text{Volume} = \frac{500 \text{ mL}}{1000} = 0.500 \text{ L} \]This simple conversion ensures you are using the correct units for molarity calculations and avoids errors in chemical computations.

Moles Calculation

Understanding how to calculate moles is a fundamental skill in chemistry, particularly when dealing with solutions. To find the number of moles of a substance, you use the formula:\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]This formula requires you to know both the mass of the substance in grams and its molar mass (g/mol). For example, with sodium thiocyanate (NaSCN):

• Mass of NaSCN: 25.0 g
• Molar Mass of NaSCN: 81.08 g/mol

Plug these into the formula:\[ \text{moles} = \frac{25.0 \, \text{g}}{81.08 \, \text{g/mol}} \approx 0.3085 \, \text{mol} \]By calculating moles, you provide a bridge between the mass of a substance and its chemical behavior in reactions, paving the way for further calculations, like determining the molarity of a solution.