Problem 77 - General Chemistry

Question

How many grams of sodium dichromate, \(\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\), should be added to a \(100.0-\mathrm{mL}\) volumetric flask to prepare \(0.025 \mathrm{M} \mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) when the flask is filled to the mark with water?

Step-by-Step Solution

Answer

You need 0.655 grams of sodium dichromate.

Step 1: Calculate the Moles Needed

To find the number of moles of sodium dichromate required, use the formula: \( n = M \times V \), where \( M \) is the molarity (0.025 M) and \( V \) is the volume in liters (0.100 L for 100 mL). \[ n = 0.025 \text{ M }\times 0.100 \text{ L } = 0.0025 \text{ mol}\]

Step 2: Calculate the Molar Mass of Sodium Dichromate

Sodium dichromate \( \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7 \) contains 2 sodium (Na), 2 chromium (Cr), and 7 oxygen (O) atoms. Using atomic masses, calculate the molar mass:\(\text{Molar mass of } \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7 = (2 \times 22.99) + (2 \times 51.996) + (7 \times 15.999) \ = 45.98 + 103.992 + 111.993 \ = 261.97 \text{ g/mol}\)

Step 3: Calculate the Mass Needed

To find the mass needed, use the formula: \( \text{mass} = n \times \text{molar mass} \), where \( n = 0.0025 \text{ mol} \) and the molar mass is 261.97 g/mol:\[\text{mass} = 0.0025 \text{ mol } \times 261.97 \text{ g/mol } = 0.654925 \text{ g}\]

Step 4: Round and Prepare the Solution

Since the calculated mass is 0.654925 g, round to three significant figures based on precision considerations: \[ \text{Mass needed} \approx 0.655 \text{ g}\]Add 0.655 grams of sodium dichromate to the 100.0 mL volumetric flask and fill it to the mark with water to make a 0.025 M solution.

Key Concepts

Understanding Sodium Dichromate

Sodium dichromate is a bright orange-red crystalline solid that is commonly used in volumetric analysis for redox reactions. It is the sodium salt of dichromic acid and is known for its strong oxidizing properties. This makes it an important chemical for industrial processes and laboratory experiments. When handling sodium dichromate, it is crucial to be cautious as it is a strong oxidizer and can be harmful if ingested or inhaled. Additionally, it is often used in solutions where precise concentration is essential for chemical reactions.

• Use: Often employed in laboratory settings for its oxidizing capabilities.
• Appearance: Recognized by its vivid orange crystalline appearance.
• Safety: Handle with care due to potential health hazards.

Understanding sodium dichromate's role in various chemical processes aids in mastering volumetric analysis and related calculations.

Molarity Calculations Simplified

Molarity is a way of expressing the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. In practice, molarity allows chemists to accurately determine how much substance is present in a given volume of liquid, which is vital for reactions requiring precise concentrations.
To calculate molarity, you use the formula:
\[ M = \frac{n}{V} \] where \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters. For example, knowing the molarity of sodium dichromate allows you to calculate how many grams you need to prepare a specific volume of a desired concentration. Here are key concepts related to molarity calculations:

• Units: Molarity is measured in moles per liter (M).
• Applications: Used to determine how much solute is required for solutions of specific concentrations.
• Conversion: Always remember to convert the volume to liters when using the formula.

By mastering molarity calculations, you're equipped to accurately prepare chemical solutions needed for experiments and analyses.

The Basics of Volumetric Analysis

Volumetric analysis is a common laboratory method used to determine the concentration of an unknown substance by reacting it with a standard solution. It involves measuring the precise volumes of liquids, hence the name "volumetric." This method is crucial in many types of chemical analyses, such as titrations. Volumetric analysis often uses a volumetric flask for preparing solutions of known concentration, ensuring precision. When preparing solutions, the following steps can be observed:

• Volume Measurement: Use precise volumetric tools like pipettes and flasks for accurate results.
• Standard Solutions: These are solutions with known concentrations and are used to determine the unknown concentrations of other solutions.
• Application Areas: Widely used for redox reactions, acid-base titrations, and chemical equilibrium studies.

Mastering volumetric analysis allows you to engage in a variety of chemical investigations, providing pivotal knowledge in both academic settings and scientific research.