Question

To obtain a solution that is $1.00\mathrm{M}{\mathrm{NaNO}}_3$, you should prepare (a) 1.00 L of aqueous solution containing $100\mathrm{g}{\mathrm{NaNO}}_3;$ (b) $1\mathrm{kg}$ of aqueous solution containing $85.0\mathrm{g}{\mathrm{NaNO}}_3;(\mathrm{c})5.00\mathrm{L}$ of aqueous solution containing $425\mathrm{g}{\mathrm{NaNO}}_3;(\mathrm{d})$ an aqueous solution containing $8.5\mathrm{mg}{\mathrm{NaNO}}_3/\mathrm{mL}$.

Short answer

The correct solution which gives 1.00 M of $NaN{O}_3$ is not provided in the options.

Step-by-step solution

- Conversion of Quantity of Solute to Moles

Using the molar mass of $NaN{O}_3$, which is 85 g/mol, convert the given quantities of $NaN{O}_3$ in each solution to moles. This is done by dividing the quantity by the molar mass.

- Implementation of the Molarity Concept

Apply the concept of molarity, which is number of moles of solute per liter of the solution. The quantity of the solution is given in different units (L, kg and mg/mL), it's crucial to convert these quantities to liters, because molarity is in moles per liter.

- Calculation and Comparison with the Desired Molarity

Caculate the molarity for each solution and compare with the desired molarity which is 1.00 M.

- Selection of the Appropriate Solution

The solution which gives the desired molarity is chosen as the correct answer. If none of the given solutions give the desired molarity, then the solution that gives a value closest to the desired molarity may be considered.

Key concepts

Molarity

Molarity is a key concept in chemistry that measures the concentration of a solution. It is specifically defined as the number of moles of solute per liter of solution. Understanding how to calculate molarity is crucial as it allows chemists to communicate concentrations accurately. The formula to determine molarity is:

• Molarity ( M ) = Moles of solute / Liters of solution.

This relationship highlights why it’s essential to ensure the volume of the solution is converted to liters, assuring that molarity calculations are consistent and reliable.
When working with molarity, keep in mind that it is always expressed in terms of liters. This requirement underlines the importance of unit conversions in chemistry, which we will explore in another section.

Moles Conversion

Converting grams of a compound to moles is a fundamental skill in chemistry. To convert grams to moles, you'll use the molar mass of the compound, which is the mass of one mole of that substance. The formula to convert grams to moles is:

• Moles = Mass of substance (g) / Molar mass (g/mol).

In the context of Sodium Nitrate ( NaNO_3 ), if you are given the mass of NaNO_3 in grams, you divide this by its molar mass (85 g/mol) to determine the number of moles. This conversion is a key step in determining the molarity of a solution.
By effectively converting grams to moles, you gain an understanding of the relationship between the amount of substance and its chemical potential in reactions. This is an essential process for calculating the concentration of a solution.

Sodium Nitrate (NaNO3)

Sodium nitrate ( NaNO_3 ) is a common chemical compound with varied applications in industry and laboratories. It is known for its usage in fertilizers, food preservation, and application in manufacturing explosives. Understanding the chemical properties and uses of NaNO_3 is important when preparing solutions.

• It is a crystalline solid, highly soluble in water.
• Molar mass: 85 g/mol, crucial for conversion calculations.

The role of Sodium Nitrate in solution preparation is pivotal due to its chemical stability and reactivity. When preparing a solution with a specific molarity, knowing the precise molar mass is necessary for accurate molarity calculations. This ensures the right amount of solute is dissolved, leading to an intended concentration.

Volume Conversion

Volume conversion is an essential task when working with solutions, particularly for determining molarity. Molarity calculations require that the volume of the solution is expressed in liters. Sometimes, you may be given a solution’s volume in milliliters (mL) or kilograms (kg). Here’s how to handle these conversions:

• To convert milliliters to liters: divide by 1,000 (since 1,000 mL = 1 L).
• For density-dependent conversions from kilograms: consider the type of solute and solvent used. For instance, assuming the solution has water as a base, know that 1 kg of water is approximately 1 liter.

Volume conversions ensure that all measurements are within the correct units for straightforward calculations. This step is vital to ensure molarity calculations are accurate and effective, allowing chemists to reach desired solution concentrations.