Question

A solution is prepared by dissolving \(95.4\) grams of sodium nitrate in 753 grams of water. (a) What is the percent sodium nitrate in the solution? (b) If 350 . grams of the solution are poured into a beaker, how many grams of sodium nitrate are introduced into the beaker? (c) How many grams of the solution are required to obtain \(50.0\) grams of sodium nitrate?

Short answer

The percent sodium nitrate in the solution is 11.3%. 39.3 grams of sodium nitrate are introduced into the beaker, and 444 grams of the solution are required to obtain 50 grams of sodium nitrate.

Step-by-step solution

Calculate the total mass of the solution

Add the mass of sodium nitrate and the mass of water together. Total mass = 95.4 grams (sodium nitrate) + 753 grams (water) = 848.4 grams.

Calculate the percent sodium nitrate in the solution

Use the formula for percentage: \[ \text{Percent Sodium Nitrate} = \frac{\text{Mass of Sodium Nitrate}}{\text{Total Mass of Solution}} \times 100 \] Substitute the values into the equation: \[ \text{Percent Sodium Nitrate} = \frac{95.4 \text{ grams}}{848.4 \text{ grams}} \times 100 \] Simplifying this gives the percent sodium nitrate.

Calculate mass of sodium nitrate in 350 grams of solution

First, determine the fraction of sodium nitrate in the solution: \[ \text{Fraction of Sodium Nitrate} = \frac{95.4 \text{ grams}}{848.4 \text{ grams}} \] Next, multiply this fraction by 350 grams: \[ \text{Mass of Sodium Nitrate} = \text{Fraction of Sodium Nitrate} \times 350 \text{ grams} \] Simplifying this calculation gives the mass of sodium nitrate.

Calculate the mass of the solution required for 50 grams of sodium nitrate

Use the mass fraction of sodium nitrate found in Step 3: \[ \text{Required mass of solution} = \frac{50.0 \text{ grams}}{\text{Fraction of Sodium Nitrate}} \] Substitute the fraction found in Step 3 to determine the required mass of the solution.

Key concepts

mass percent calculation

One of the fundamental tasks in chemistry is calculating the mass percent of a component in a solution. Here's a step-by-step guide to help you understand.
To start, you need to know the formula for mass percent, which is: \[ \text{Mass percent} = \frac{ \text{Mass of solute} }{ \text{Mass of solution} } \times 100 \]
In our exercise, the solute is sodium nitrate. The solvent is water, and their masses are provided. The first step is to find the total mass of the solution, calculated as follows:
\[ \text{Total mass} = \text{mass of sodium nitrate} + \text{mass of water} = 95.4 \text{ grams} + 753 \text{ grams} = 848.4 \text{ grams} \]
After confirming the calculation, we can now find the mass percent of sodium nitrate using the formula mentioned above. Substituting the values:
\[ \text{Percent Sodium Nitrate} = \frac{95.4 \text{ grams}}{848.4 \text{ grams}} \times 100 = 11.24\text{\%} \]
This value means that in every 100 grams of the solution, there are 11.24 grams of sodium nitrate. The concept of mass percent is crucial for understanding how much of a substance is present in a mixture.

solution concentration

Solution concentration is another important concept in chemistry. It describes how much solute is present in a given quantity of solvent or solution. Various ways to express concentration include molarity, molality, and mass percent.
In our exercise, we use mass percent, but let's focus on understanding what's happening when we deal with solution concentrations.
For example, after calculating the percent composition, we can use this concentration to find out how much solute (sodium nitrate) is present in a specific portion of the solution.
If you pour 350 grams of this solution into a beaker, how do you find out how many grams of sodium nitrate have been introduced?
First, calculate the fraction of sodium nitrate in the total solution: \[ \text{Fraction of Sodium Nitrate} = \frac{95.4 \text{ grams}}{848.4 \text{ grams}} = 0.1124 \]
Next, multiply this fraction by the total mass of the portion poured into the beaker: 350 grams.
\[ \text{Mass of Sodium Nitrate} = 0.1124 \times 350 \text{ grams} = 39.34 \text{ grams} \]
Thus, in 350 grams of the solution, there are 39.34 grams of sodium nitrate. Understanding solution concentration helps us determine how much solute is present in varying amounts of solution, a vital aspect in many chemical applications.

problem-solving in chemistry

Problem-solving in chemistry often involves applying various principles and mathematical formulas to find specific information. Let's explore how we approach these problems using our example.
Initially, identify what is known and what needs to be found. In our case, we're given the masses of sodium nitrate and water and need to find percent composition and various mass-related calculations.
Follow these steps for effective problem-solving in chemistry:

• Identify the known values and the unknown values.
• Write down relevant formulas (e.g., mass percent formula).
• Substitute the known values into the formulas to find the unknown values.
• Perform each step accurately, ensuring no calculation errors.

Now, if we need to find how much of the solution is required to obtain a specific amount of solute (such as 50.0 grams of sodium nitrate), use the relationship we found earlier:
\[ \text{Required mass of solution} = \frac{50.0 \text{ grams}}{0.1124} = 445 \text{ grams} \]
Therefore, we would need 445 grams of the solution to get 50.0 grams of sodium nitrate.
Problem-solving in chemistry involves understanding concepts, applying formulas correctly, and performing precise calculations. By breaking down problems into manageable steps, we can effectively tackle complex chemistry questions.