Question

Molarity and molality of a solution of an liquid (mol. wt. \(=50\) ) in aquous solution is 9 and 10 respectively. What is the density of solution? (a) \(1 \mathrm{~g} / \mathrm{cc}\) (b) \(0.95 \mathrm{~g} / \mathrm{cc}\) (c) \(1.05 \mathrm{~g} / \mathrm{cc}\) (d) \(1.35 \mathrm{~g} / \mathrm{cc}\)

Short answer

The density of the solution is 1.35 g/cc.

Step-by-step solution

Understanding Molarity

Molarity (M) is the number of moles of solute per liter of solution. For the liquid in the question, it's given as 9 M. This means there are 9 moles of the solute in 1 liter of the solution.

Understanding Molality

Molality (m) is the number of moles of solute per kilogram of solvent. It's given as 10 m, which means there are 10 moles of the liquid solute per kilogram of water.

Calculating Moles of Solute in 1 Liter of Solution

Since the molarity is 9 M, we have 9 moles of solute present in 1 liter of the solution.

Finding Mass of Solute

Using the molar mass (50 g/mol), we can find the mass of the solute in 1 liter of solution. Mass of solute = Number of moles x Molar mass = 9 moles x 50 g/mol = 450 g.

Calculating Mass of Solvent in Solution

Since the molality is 10 m and we have 9 moles in 1 liter of the solution, we can calculate the mass of the water (solvent) using the definition of molality. Mass of solvent = Number of moles / Molality = 9 moles / 10 m = 0.9 kg or 900 g of solvent.

Calculating Total Mass of the Solution

Total mass of the solution is the sum of the mass of the solute and the solvent. Total mass = Mass of solute + Mass of solvent = 450 g + 900 g = 1350 g.

Finding Density of the Solution

Density is mass per unit volume. We know the total mass of the solution and, by definition of molarity, we have a total volume of 1 liter (or 1,000 cc). Density = Total mass / Volume = 1350 g / 1000 cc = 1.35 g/cc.

Key concepts

Molarity

Molarity is a measure of how concentrated a solution is. To visualize this, imagine a lemonade stand where the lemonade is made by mixing a certain amount of lemon juice (the solute) with water (the solvent). The molarity tells us how many lemons' worth of juice is in every liter of the mixture. If we say the lemonade has a molarity of 9 M, like the liquid in our exercise, it's like saying we squeezed 9 lemons into every liter of water. This concept is essential when chemists need to know how concentrated a solution is to predict how it will react in different scenarios.

This information allows them to replicate experiments accurately or to scale reactions up or down without changing the proportions and behavior of the substances involved. In experiments and industrial processes, achieving the desired concentration can be the difference between success and a mess! Because molarity is dependent on the volume of the solution, changes in temperature or pressure might affect it, since these conditions can cause the solution's volume to expand or contract.

Molality

Molality is a lesser-known cousin of molarity but no less important. It's the mojito to your lemonade, if you will—another way of measuring concentration, but instead of looking at the volume of the solution, we look at the mass of the solvent. For example, if you are making a mojito and you want to ensure the drink has a consistent strength no matter the size of the ice cubes, you would base your rum measurement by the weight of the mint leaves and lime juice rather than the total volume of liquid.

In our exercise, a molality of 10 m means that there are 10 moles of our 'lemon juice' in every kilogram of 'water'. Because it is based on mass, molality does not change with temperature or pressure, making it very useful for experiments conducted under varying conditions. It keeps the strength of your 'mojito' consistent, whether it’s served on a hot beach or in a chilly mountain resort.

Molar Mass

The molar mass is like the ID card of a substance, telling you how much one mole of that substance weighs. Returning to our lemonade stand, if we know that one lemon weighs 50 grams, we could say that the 'molar mass' of our lemons is 50 g/mol. In chemistry, molar mass allows scientists to convert between the weight of a substance and the number of moles, which is how chemists prefer to measure amounts of substances. It's a key part of understanding recipes in both the kitchen and the lab.

In the scenario described in the exercise, we're dealing with a substance of 50 g/mol molar mass. So if we know we have 9 moles of this substance in our lemonade (from the molarity), we can calculate that we essentially have 9 lemons, each weighing 50 grams. This straightforward conversion (9 moles times 50 g/mol) is how we determined the total weight of lemon juice in our lemonade, which was 450 grams.