4.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The molarity of the s

Q: Why do we have to divide the volume by 1000?

The standard definition of Molarity requires the volume of the solution to be in Liters (L). Since the problem gives the volume in milliliters (mL), we must divide by 1000 to convert it to Liters ($1\text{ L} = 1000\text{ mL}$).

Q: What is the difference between Molarity and Molality?

Molarity (M) is the number of moles of solute per Liter of **solution** (volume-based). Molality (m) is the number of moles of solute per Kilogram of **solvent** (mass-based). Molarity changes with temperature because volume expands/contracts, but molality remains constant.

Q: Why did we write 0.2 as $2 \times 10^{-1}$?

The question specifically asked for the answer in the format $x \times 10^{-1}$. Writing $0.2$ in scientific notation as $2 \times 10^{-1}$ allows us to directly compare it to the given format and easily identify that $x = 2$.

Q: Does it matter what Compound A actually is?

For this specific calculation, no. As long as we know the mass of the compound and its molar mass, we can calculate the number of moles. The chemical identity of the compound doesn't change the math.

Q: What if the volume was given in cubic centimeters ($cm^3$)?

One cubic centimeter ($1\text{ cm}^3$) is exactly equal to one milliliter ($1\text{ mL}$). So, if the volume was $250\text{ cm}^3$, the calculation would be exactly the same.

Question

4.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The molarity of the solution in M is $x 	imes 10^{-1}$. The value of $x$ is ......... . (Rounded off to the nearest integer).

Sigma Percentile · Accepted Answer

### The Essence of Concentration

When we talk about solutions in chemistry, we are essentially talking about a crowd of solute particles swimming in a sea of solvent. But how crowded is it? That's exactly what **concentration** tells us. One of the most fundamental and widely used ways to express this crowdedness is **Molarity**.

Imagine you are making a cup of coffee. The amount of coffee powder you add to a specific volume of water determines how strong the coffee will be. In the language of chemistry, the coffee powder is the solute, the water is the solvent, and the final drink is the solution. Molarity gives us a precise mathematical way to state this "strength."

### Analyzing the Setup

In our problem, we are given a beaker containing an aqueous solution. We know two critical pieces of information about the solute (Compound A):
1. Its mass, $W = 4.5	ext{ g}$
2. Its molar mass, $M_w = 90	ext{ g/mol}$

We also know the total volume of the solution, $V = 250	ext{ mL}$. Our mission is to find the molarity of this solution and express it in a specific scientific notation format.

### The Master Equation

Molarity ($M$) is defined as the number of moles of solute dissolved per liter of the solution. The formula is beautifully simple:

$$M = \frac{	ext{Moles of solute } (n)}{	ext{Volume of solution in Liters } (V_L)}$$

To use this formula, we need to prepare our ingredients. First, we need the moles of the solute. Moles can be found by dividing the given mass by the molar mass:

$$n = \frac{W}{M_w} = \frac{4.5}{90} = 0.05	ext{ mol}$$

Next, we need the volume of the solution in liters. Since it's given in milliliters, we simply divide by $1000$:

$$V_L = \frac{250}{1000} = 0.25	ext{ L}$$

### Final Calculation

Now, we bring our prepared ingredients back to the master equation. We substitute the moles and the volume into the molarity formula:

$$M = \frac{0.05}{0.25}$$

To make the math easier, we can shift the decimal point two places to the right in both the numerator and the denominator. This gives us:

$$M = \frac{5}{25} = \frac{1}{5} = 0.2	ext{ M}$$

We have found the molarity! It is $0.2	ext{ M}$. However, the question has a slight twist. It asks us to express the molarity in the form of $x 	imes 10^{-1}$.

Let's convert our answer into scientific notation:

$$0.2 = 2 	imes 10^{-1}$$

By comparing our result with the given expression $x 	imes 10^{-1}$, it becomes crystal clear that the value of $x$ is exactly **$2$**.

This problem is a perfect example of how fundamental definitions in chemistry translate into straightforward mathematical steps. Always remember to keep an eye on your units, especially converting milliliters to liters, as that is where most silly mistakes happen!

Animated Solution for Chemistry - Basic Concepts in Chemistry: 4.5 g of compound A (MW = 90) was used to make 250 mL of its aqueous solution. The molarity of the solution in M is $x \times 1 0^{- 1}$ . The value of $x$ is ......... . (Rounded off to the nearest integer).

Enter Numerical Value:

Visualized Solution

\text{Visualizing the Solution}

\text{Formula for Molarity}

\text{Substituting the Values}

\text{Calculating Moles and Volume}

\text{Calculating Molarity}

\text{Finding the value of } x

\text{What's Next?}

The Sigma Insight: Molecular Mass, Mole Concept and Concentration

The Essence of Concentration

Analyzing the Setup

The Master Equation

Final Calculation

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