H2O Mass Calculation: Grams In 7.2 X 10^23 Molecules

Hey guys! Ever wondered how to calculate the mass of a specific number of water molecules? It's a classic chemistry problem, and we're going to break it down step-by-step. The question we're tackling today is: What is the mass in grams of 7.2 x 10^23 molecules of H2O, considering that the molar mass of water is approximately 18 g/mol? Let's dive in and solve this problem together!

Understanding the Basics

Before we jump into the calculation, let's make sure we're all on the same page with a few key concepts. This will make the process much smoother and easier to understand. So, what do we need to know?

Molar Mass

Molar mass is a fundamental concept in chemistry. It represents the mass of one mole of a substance, expressed in grams per mole (g/mol). For water (H2O), the molar mass is approximately 18 g/mol. This means that one mole of water molecules weighs 18 grams. The molar mass is derived from the atomic masses of the elements in the compound (in this case, hydrogen and oxygen) and is crucial for converting between mass and moles.

Avogadro's Number

Another critical concept is Avogadro's number, which is approximately 6.022 x 10^23. This number represents the number of entities (atoms, molecules, ions, etc.) in one mole of a substance. So, one mole of anything contains 6.022 x 10^23 of those things. Avogadro's number serves as a bridge between the macroscopic world (grams) and the microscopic world (number of molecules).

The Mole Concept

The mole is the SI unit for the amount of substance. It's a convenient way to count large numbers of atoms or molecules. Just like we use "dozen" to represent 12 items, we use "mole" to represent 6.022 x 10^23 items. Understanding the mole concept is essential for stoichiometric calculations and converting between mass, moles, and number of particles.

Step-by-Step Calculation

Now that we've reviewed the basics, let's get to the calculation. We want to find the mass in grams of 7.2 x 10^23 molecules of water. Here’s how we can do it:

Step 1: Convert Molecules to Moles

First, we need to convert the number of water molecules to moles. To do this, we'll use Avogadro's number as a conversion factor.

$$\text{Moles of H2O} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}$$

$$\text{Moles of H2O} = \frac{7.2 \times 10^{23}}{6.022 \times 10^{23}}$$

$$\text{Moles of H2O} \approx 1.195 \, \text{mol}$$

So, 7.2 x 10^23 molecules of H2O is approximately 1.195 moles.

Step 2: Convert Moles to Grams

Next, we'll convert the moles of water to grams using the molar mass of water (18 g/mol).

$$\text{Mass of H2O} = \text{Moles of H2O} \times \text{Molar mass of H2O}$$

$$\text{Mass of H2O} = 1.195 \, \text{mol} \times 18 \, \text{g/mol}$$

$$\text{Mass of H2O} \approx 21.51 \, \text{g}$$

Therefore, the mass of 7.2 x 10^23 molecules of H2O is approximately 21.51 grams.

Analyzing the Answer Choices

Now, let's look at the answer choices provided:

• A) 18 g
• B) 36 g
• C) 54 g
• D) 72 g

Our calculated mass is approximately 21.51 grams, which doesn't directly match any of the provided options. However, let's re-evaluate our calculation and see if we can find any discrepancies.

Re-evaluating the Calculation

Going back to our initial steps, we converted the number of molecules to moles and then moles to grams. Let's double-check our math:

$$\text{Moles of H2O} = \frac{7.2 \times 10^{23}}{6.022 \times 10^{23}} \approx 1.195 \, \text{mol}$$

$$\text{Mass of H2O} = 1.195 \, \text{mol} \times 18 \, \text{g/mol} \approx 21.51 \, \text{g}$$

It seems our calculation is correct. However, since we need to choose from the given options, we should consider if there was any approximation made that significantly affected the result. The closest answer to our calculated value (21.51 g) is not among the options. Let's re-examine the question and the possible answers again.

Spotting an Error

Okay, guys, I think I might have spotted a mistake in my initial approach. The question asks for the mass of 7.2 x 10^23 molecules, and we're given that the molar mass of water is 18 g/mol. Instead of directly calculating, let’s think proportionally. We know that 6.022 x 10^23 molecules (1 mole) weigh 18 g. We have more than one mole, but let’s see if any of the answers can be derived with a simpler approach.

Let's try to find a ratio that makes sense with the options. Suppose we are aiming for option D) 72 g, can that be achieved?

If 6.022 x 10^23 molecules weigh 18 g, how many times more molecules are there in 72 g?

$$\text{Ratio} = \frac{72 \, \text{g}}{18 \, \text{g}} = 4$$

So, 72 g would be 4 times the mass of 1 mole.

Now let's multiply Avogadro's number by 4:

$$4 \times (6.022 \times 10^{23}) = 24.088 \times 10^{23}$$

This is not equal to 7.2 x 10^23. So option D is not the correct one.

How about option C) 54 g?

$$\text{Ratio} = \frac{54 \, \text{g}}{18 \, \text{g}} = 3$$

$$3 \times (6.022 \times 10^{23}) = 18.066 \times 10^{23}$$

Again, this doesn't match 7.2 x 10^23.

How about option B) 36 g?

$$\text{Ratio} = \frac{36 \, \text{g}}{18 \, \text{g}} = 2$$

$$2 \times (6.022 \times 10^{23}) = 12.044 \times 10^{23}$$

Still not the right answer.

Now, let's go back to the original calculation but this time, let’s approximate Avogadro’s number to 6 x 10^23 to see if we can match one of the answer choices.

$$\text{Moles of H2O} = \frac{7.2 \times 10^{23}}{6 \times 10^{23}} = 1.2 \, \text{mol}$$

$$\text{Mass of H2O} = 1.2 \, \text{mol} \times 18 \, \text{g/mol} = 21.6 \, \text{g}$$

Still no direct match.

Considering a Possible Misprint

It's possible that there might be a misprint in the question or the answer choices. Given the options, let's consider what number of molecules would give us one of the provided masses. Since 18 g corresponds to 6.022 x 10^23 molecules, we can analyze the other options similarly.

Let's Assume Option D is the Answer If we suppose the answer is D) 72 g, then let's calculate the number of moles:

$$\text{Moles of H2O} = \frac{72 \, \text{g}}{18 \, \text{g/mol}} = 4 \, \text{mol}$$

$$\text{Number of molecules} = 4 \, \text{mol} \times (6.022 \times 10^{23} \, \text{molecules/mol}) = 24.088 \times 10^{23} \, \text{molecules}$$

The Most Likely Scenario Given the constraints and the likely intended simplicity of the question, it's plausible that the number of molecules was intended to be a simple multiple of Avogadro's number to align with one of the answer choices. Without additional information or clarification, the closest logical approach is to consider the possibility of a misprint or a simplified problem setup.

Final Answer

After carefully re-evaluating the question, calculations, and answer choices, it appears there might be an issue with the provided options or the initial problem statement. Based on the calculations and given options, none of the answers perfectly match. It is best to double-check the original problem or consult with an instructor or reliable source for clarification.

Therefore, without a perfect match, this question cannot be definitively answered with the provided options.