https://file.aiquickdraw.com/mathbot/file/1727939105199a4q2b6c9.jpg

The problem asks to calculate how many mL of a 2.6% (m/v) NaNO₃ solution are required to contain 7.4 g of sodium nitrate (NaNO₃). Here's how we can solve this:

### Step 1: Understand the concentration formula
The percentage given is a mass/volume (m/v) percentage. This means:
\[
2.6\% \ (\text{m/v}) = \frac{2.6 \ \text{g of NaNO}_3}{100 \ \text{mL of solution}}
\]

### Step 2: Set up the proportion
We are asked how many mL of solution contain 7.4 g of NaNO₃. Using the ratio from the concentration definition, we can set up a proportion:
\[
\frac{2.6 \ \text{g}}{100 \ \text{mL}} = \frac{7.4 \ \text{g}}{x \ \text{mL}}
\]

### Step 3: Solve for \(x\)
Cross-multiply to solve for \(x\):
\[
2.6x = 7.4 \times 100
\]
\[
2.6x = 740
\]
\[
x = \frac{740}{2.6} = 284.62 \ \text{mL}
\]

### Step 4: Significant Figures
The given data has two significant figures (7.4 g and 2.6%), so the final answer should be rounded to **two significant figures**:
\[
x \approx 2.8 \times 10^2 \ \text{mL} \ (\text{or } 280 \ \text{mL})
\]

### Final Answer:
The solution would contain approximately **280 mL** of the 2.6% NaNO₃ solution to have 7.4 g of sodium nitrate.

Would you like further details on any step? Here are some related questions to consider:

1. How would the calculation change if the concentration were given in molarity instead of percentage?
2. What is the molar mass of sodium nitrate (NaNO₃)?
3. How do you handle more complex percentage concentrations like mass/volume/volume?
4. How can we calculate the mass of solute in a given volume for any percentage concentration?
5. What units would you use if this were a molarity problem instead of mass/volume?

**Tip:** When working with percentages, always ensure that your units match across the problem (grams with grams, mL with mL).

How many mL of 2.6% (m/v) NaNO₃ solution would contain 7.4 g of sodium nitrate? Be sure your answer has the correct number of significant figures.

Learn how to determine the volume in mL of a 2.6% (m/v) NaNO₃ solution that would contain 7.4 g of sodium nitrate. The problem covers the use of proportions, percentage solutions, and rounding to the correct significant figures. Ideal for high school chemistry students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation