Q1. How many moles of gas are in a 5.0 L sample at 2.0 atm and 300 K?

Background

Topic: Ideal Gas Law

This question is testing your ability to apply the ideal gas law to solve for the number of moles (n) of a gas using pressure, volume, and temperature. Understanding how these variables relate to each other is fundamental to working with gas behavior under various conditions.

Key formula:

Where:

• P = pressure (in atm)

• V = volume (in liters)

• n = number of moles (what you're solving for)

• R = ideal gas constant = 0.0821 L·atm/mol·K

• T = temperature in Kelvin

Step-by-Step Guidance

1. Identify the known values and what you're solving for:

   Start by extracting all the information given in the problem. Look for pressure (P), volume (V), temperature (T), and identify what quantity you need to find. In this case, you're solving for the number of moles (n). Make sure to note the units for each value, as they must be consistent with the gas constant you'll use.

2. Select the appropriate formula:

   The ideal gas law relates pressure, volume, temperature, and the number of moles. This is the fundamental equation you'll need to solve this problem. The ideal gas law states that the product of pressure and volume is proportional to the number of moles and temperature. Recognize that this equation allows you to calculate any one variable if you know the other three.

   where is the ideal gas constant. You'll need to choose the correct value of that matches your units (atm, L, mol, K).

3. Rearrange the equation to solve for the unknown:

   Since you're solving for , you need to isolate it on one side of the equation. Divide both sides of the ideal gas law equation by to get by itself. This algebraic manipulation allows you to express the number of moles in terms of the other variables. The reasoning here is that if , then dividing both sides by will isolate .

4. Verify unit consistency:

   Before substituting values, check that all units are compatible. The pressure is in atm, volume in liters, and temperature in Kelvin. You'll need to use the gas constant that has units of to ensure the units cancel correctly and give you moles as the final unit. This dimensional analysis step is crucial to avoid calculation errors.

5. Set up the calculation:

   Substitute your known values into the rearranged equation. Write out the complete expression with all values in place, including the appropriate gas constant value. This setup shows you exactly what calculation needs to be performed. Make sure to use the correct numerical value for that matches your unit system.

   Now substitute your specific values and the correct gas constant, then perform the arithmetic to find the number of moles. Remember to follow the order of operations when evaluating the expression.

Try solving on your own before revealing the answer!

Q2. What is the molarity of a solution prepared by dissolving 58.5 g of NaCl in enough water to make 500 mL of solution?

Background

Topic: Molarity and Solution Concentration

This question is testing your understanding of molarity, which is a way to express the concentration of a solution. Molarity represents the number of moles of solute per liter of solution and is one of the most common units used in chemistry for expressing solution concentrations.

Key formula:

where is molarity, is moles of solute, and is volume in liters.

Where:

• M = molarity (moles per liter, mol/L)

• n = number of moles of solute

• V = volume of solution in liters

• m = mass of solute (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 molarity (M) of the solution. The problem provides the mass of NaCl (58.5 g) and the volume of the solution (500 mL). Note that the volume is given in milliliters, which you'll need to convert to liters for the molarity calculation.

2. Convert volume to liters:

   Since molarity is defined as moles per liter, you must convert the volume from milliliters to liters. This conversion is essential because the molarity formula requires volume in liters. Remember that 1 L = 1000 mL, so you'll divide the volume in milliliters by 1000.

3. Calculate the molar mass of NaCl:

   To find the number of moles, you need the molar mass of NaCl. The molar mass is the sum of the atomic masses of all atoms in the compound. Look up the atomic masses: Na (sodium) and Cl (chlorine) from the periodic table, then add them together to get the molar mass in grams per mole.

4. Convert mass to moles:

   Use the molar mass to convert the given mass of NaCl to moles. The relationship between mass, moles, and molar mass is: moles = mass divided by molar mass. This conversion is necessary because molarity requires moles, not grams.

   Substitute the mass and molar mass values you've identified to calculate the number of moles.

5. Calculate molarity:

   Now that you have the number of moles and the volume in liters, you can calculate the molarity using the formula. Divide the number of moles by the volume in liters. This will give you the concentration in moles per liter.

   Substitute your calculated values for moles and volume (in liters) to find the final molarity.

Try solving on your own before revealing the answer!

Q3. Calculate the heat energy required to raise the temperature of 250 g of water from 20°C to 80°C. The specific heat capacity of water is 4.18 J/g·°C.

Background

Topic: Heat Transfer and Specific Heat Capacity

This question is testing your understanding of heat energy calculations using the specific heat capacity formula. When you heat a substance, the amount of energy required depends on the mass of the substance, the temperature change, and the substance's specific heat capacity, which is a measure of how much energy is needed to raise the temperature of 1 gram of the substance by 1 degree Celsius.

Key formula:

Where:

• q = heat energy (in joules, J)

• m = mass of the substance (in grams, g)

• c = specific heat capacity (in J/g·°C)

• ΔT = change in temperature (final temperature - initial temperature, in °C)

Step-by-Step Guidance

1. Identify the known values and what you're solving for:

   You need to find the heat energy (q) required. The problem provides the mass of water (250 g), the initial temperature (20°C), the final temperature (80°C), and the specific heat capacity of water (4.18 J/g·°C). Make sure you understand what each variable represents in the context of heat transfer.

2. Calculate the temperature change (ΔT):

   The temperature change is the difference between the final and initial temperatures. This value is crucial because the heat energy is directly proportional to how much the temperature changes. Subtract the initial temperature from the final temperature to find ΔT.

   Substitute your known temperature values to calculate the change in temperature.

3. Verify units are consistent:

   Before proceeding with the calculation, ensure all units are compatible. The mass is in grams, specific heat capacity is in J/g·°C, and temperature change will be in °C. When you multiply these together, the grams and °C units will cancel, leaving you with joules (J) as the final unit, which is correct for heat energy.

4. Set up the heat energy calculation:

   Use the specific heat capacity formula to set up your calculation. The formula relates heat energy to mass, specific heat capacity, and temperature change. Write out the complete expression with all your known values substituted into the formula.

   Substitute the mass, specific heat capacity, and the temperature change you calculated in the previous step.

5. Perform the calculation:

   Multiply the values together following the order of operations. First, you might find it helpful to multiply the mass and specific heat capacity, then multiply that result by the temperature change. Alternatively, you can multiply all three values together in one step. Make sure to keep track of units as you calculate.

   Complete the arithmetic to find the heat energy in joules.

Try solving on your own before revealing the answer!