Q1. What volume will 0.50 moles of gas occupy at STP (Standard Temperature and Pressure)?

Background

Topic: Molar Volume at STP

This question tests your understanding of the relationship between moles and volume at standard conditions. At STP, one mole of any ideal gas occupies a specific volume, which is a fundamental concept in gas stoichiometry and volume calculations.

Key formula:

where is the molar volume at STP.

Where:

• V = volume (in liters, L)

• n = number of moles

• V_m = molar volume at STP = 22.4 L/mol

• STP = Standard Temperature and Pressure (0°C and 1 atm)

Step-by-Step Guidance

1. Identify what you know and what you're solving for:

   You need to find the volume (V) that 0.50 moles of gas will occupy. The problem states the conditions are STP, which means you can use the standard molar volume. Recognize that at STP, all ideal gases have the same molar volume regardless of their identity.

2. Recall the molar volume at STP:

   At standard temperature and pressure (0°C and 1 atm), one mole of any ideal gas occupies 22.4 liters. This is a constant value that applies to all ideal gases under these specific conditions. This value comes from experimental measurements and is fundamental to gas calculations.

3. Set up the volume calculation:

   Since you know the number of moles and the volume per mole, you can calculate the total volume by multiplying these values. The relationship is straightforward: total volume equals the number of moles times the volume per mole.

   Substitute your known values into this equation.

4. Verify the units:

   Check that your units will work out correctly. When you multiply moles by liters per mole, the moles cancel out, leaving you with liters as the final unit, which is correct for volume.

5. Perform the calculation:

   Multiply the number of moles by the molar volume at STP. This will give you the volume in liters that the gas occupies under standard conditions.

   Complete the arithmetic to find the final volume.

Try solving on your own before revealing the answer!

Q2. How many grams of NaOH are needed to prepare 250 mL of a 0.100 M solution?

Background

Topic: Solution Preparation and Molarity

This question tests your ability to work backwards from molarity to determine the mass of solute needed. You'll need to convert between moles and mass using molar mass, and understand how molarity relates to the amount of solute in a given volume of solution.

Key formula:

and

Where:

• M = molarity (mol/L)

• n = number of moles

• V = volume in liters

• m = mass in grams

• MM = molar mass (g/mol)

Step-by-Step Guidance

1. Identify what you're solving for and the given information:

   You need to find the mass (m) of NaOH required. The problem provides the desired molarity (0.100 M) and the volume of solution (250 mL). Note that you'll need to convert the volume to liters and calculate the molar mass of NaOH.

2. Convert volume to liters:

   Since molarity is defined in terms of liters, convert the volume from milliliters to liters. This conversion is essential for using the molarity formula correctly.

3. Calculate the number of moles needed:

   Rearrange the molarity formula to solve for moles. Since , you can multiply both sides by volume to get . This tells you how many moles of NaOH are required for the solution.

   Substitute your molarity and volume (in liters) to find the number of moles.

4. Determine the molar mass of NaOH:

   Calculate the molar mass by adding the atomic masses of sodium (Na), oxygen (O), and hydrogen (H). Look up these values from the periodic table and sum them to get the molar mass in grams per mole.

5. Convert moles to mass:

   Use the relationship between mass, moles, and molar mass. Rearrange to solve for mass: . Multiply the number of moles you calculated by the molar mass to find the required mass in grams.

   Substitute your calculated moles and molar mass to find the final answer.

Try solving on your own before revealing the answer!

Q3. What is the pH of a solution with a hydrogen ion concentration of M?

Background

Topic: pH and Acidity

This question tests your understanding of pH, which is a logarithmic scale used to express the acidity or basicity of a solution. The pH is calculated from the hydrogen ion concentration and provides a convenient way to describe how acidic or basic a solution is.

Key formula:

Where:

• pH = potential of hydrogen (unitless scale from 0-14)

• [H⁺] = hydrogen ion concentration (in mol/L or M)

• log = logarithm base 10

Step-by-Step Guidance

1. Identify what you're solving for and the given information:

   You need to calculate the pH of the solution. The problem provides the hydrogen ion concentration in scientific notation. Make sure you understand that pH is a logarithmic function, which means small changes in [H⁺] result in significant changes in pH.

2. Understand the pH formula:

   The pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration. This formula converts the concentration, which can span many orders of magnitude, into a more manageable scale from 0 to 14.

3. Substitute the concentration into the formula:

   Replace [H⁺] in the formula with the given concentration value. You'll be taking the logarithm of , which is 0.001 in decimal form.

4. Calculate the logarithm:

   When dealing with scientific notation in logarithms, remember that . For , the logarithm is -3. This is because and .

   Calculate to find its value.

5. Apply the negative sign:

   After calculating the logarithm, apply the negative sign from the pH formula. This will give you the final pH value. Remember that pH values less than 7 indicate acidic solutions, while values greater than 7 indicate basic solutions.

   Complete the calculation:

Try solving on your own before revealing the answer!