Problem 158 - A Complete Resource Book in Chemistry for JEE Main

Question

Two solutions of a substance (non-electrolyte) are mixed in the following manner. \(480 \mathrm{~mL}\) of \(1.5 \mathrm{M}\) first solution \(+520 \mathrm{~mL}\) of \(1.2 \mathrm{M}\) second solution. What is the molarity of the final mixture? [2005] (a) \(1.344 \mathrm{M}\) (b) \(2.70 \mathrm{M}\) (c) \(1.50 \mathrm{M}\) (d) \(1.20 \mathrm{M}\)

Step-by-Step Solution

Answer

The molarity of the final mixture is 1.344 M (option a).

Step 1: Calculate Moles of Solute in First Solution

Identify the volume and molarity of the first solution. The volume given is 480 mL, which is 0.480 L in liters. Use the formula for moles: Moles = Molarity \(\times\) Volume in liters. For the first solution:\[ \text{Moles} = 1.5 \, \text{M} \times 0.480 \, \text{L} = 0.72 \, \text{moles} \]

Step 2: Calculate Moles of Solute in Second Solution

Identify the volume and molarity of the second solution. The volume given is 520 mL, which is 0.520 L in liters. Use the same formula for moles as in step one. For the second solution:\[ \text{Moles} = 1.2 \, \text{M} \times 0.520 \, \text{L} = 0.624 \, \text{moles} \]

Step 3: Calculate Total Moles of Solute

Add the moles of solute calculated from both solutions to find the total number of moles after mixing.\[ \text{Total Moles} = 0.72 \, \text{moles} + 0.624 \, \text{moles} = 1.344 \, \text{moles} \]

Step 4: Calculate Total Volume of the Mixture

Add the volumes of the two solutions to find the total volume of the mixture. Convert milliliters to liters.\[ \text{Total Volume} = 0.480 \, \text{L} + 0.520 \, \text{L} = 1.000 \, \text{L} \]

Step 5: Calculate Molarity of the Final Mixture

Use the formula for molarity: Molarity = Total Moles / Total Volume.\[ \text{Molarity} = \frac{1.344 \, \text{moles}}{1.000 \, \text{L}} = 1.344 \, \text{M} \]

Key Concepts

Non-Electrolyte Solution

A non-electrolyte solution is a type of solution where the solute, when dissolved in water, does not produce ions. This means it does not conduct electricity. A classic example is sugar dissolved in water. When we talk about non-electrolyte solutions, we're typically referring to substances like sugars or alcohols that dissolve but do not disassociate into ions.
Why is this important? Well, the behavior of these solutions impacts properties like boiling point, freezing point, and, importantly for us, calculations involving molarity. Understanding whether a solution is a non-electrolyte or an electrolyte helps in accurately predicting the behavior of the solution when mixed or subjected to conditions like temperature changes.

Calculation of Moles

The calculation of moles is an essential concept in chemistry, especially when dealing with solutions. Moles are a unit used to express amounts of a chemical substance. The number of moles of a substance in a solution can be determined using the formula: \[\text{Moles} = \text{Molarity} \times \text{Volume (in liters)}\]
Why does this matter? Knowing the number of moles helps in quantifying the exact amount of solute present in a solution. This is fundamental when you are trying to understand the molarity of a solution after mixing, as molarity is directly related to how many moles of solute are within a certain volume.

• First, convert any volume given in milliliters to liters by dividing by 1000, since molarity is expressed in terms of liters.
• Then, multiply the molarity (given as M) by the volume in liters to get the moles.

Knowing how to calculate moles allows chemists to determine the concentration of solutions, make predictions about reactions, and scale their work appropriately.

Solutions Mixing

When you mix two solutions, it's crucial to consider what happens to the concentration and volume of the solutes involved. In this context, solutions mixing means combining two different solutions to form a new mixture with potentially different properties.
The primary focus in our example is understanding how to compute the new molarity after mixing. This requires calculating the total moles of solute, as the characteristic of a solution after mixing is determined by how the solutes from each solution sum up.

• Add the moles of solute from each solution to get the total moles in the mixture.
• Ensure the volumes are also combined to find the total volume of the solution post-mixing.

Understanding solutions mixing is key in fields like biochemistry and pharmacology, where precise concentrations are crucial in experiments and formulations.

Volume Conversion

Volume conversion is a straightforward yet vital concept in chemistry, especially when dealing with solutions. Solutions often have their volumes expressed in milliliters, but calculations for molarity require liters.
To convert milliliters to liters, divide the number of milliliters by 1000. For example, 480 mL becomes 0.480 L.
Why is this conversion important?

• Molarity, defined as moles per liter of solution, necessitates that volumes be in liters for accurate calculation.
• Without correct conversion, calculations can result in significant errors, leading to incorrect results and predictions.

So, always ensure that before you start any work involving molarity, the volumes you use are expressed in liters. This practice will help avoid confusion and prevent any miscalculation in the concentration of your solutions.