Chemistry - The First Law of Thermodynamics and the Heat Equation

Energy is the universe’s most stubborn currency—it can be moved, traded, or changed into a different form, but it can never be created out of thin air or truly destroyed. For a high school chemist, understanding how energy flows in a system is the difference between a successful experiment and an unexpected boom.

The First Law of Thermodynamics is essentially the Law of Conservation of Energy applied to heat and work. It tells us that the change in the internal energy of a system (delta U) is the sum of the heat (q) added to the system and the work (w) done on or by the system. The formula is: delta U = q + w.

Heat (q) is thermal energy transferred between objects due to a temperature difference. Work (w) is energy used to move something, like a piston in an engine. In most chemistry labs, we focus primarily on the heat component. If a reaction releases heat, it is exothermic; if it absorbs heat, it is endothermic.

To calculate exactly how much energy is being transferred as heat during a temperature change, we use the Specific Heat Equation: q = (m) (c) (delta T).

In this equation, q is the amount of heat measured in Joules (J). The variable m is the mass of the substance measured in grams (g). The variable c is the specific heat capacity, measured in J/gC. This is a unique thermal personality for every substance—water has a very high specific heat, while metals have very low ones. Finally, delta T is the change in temperature, calculated as the final temperature minus the initial temperature. Equation: delta T = final temp - initial temp

Practice Problems

1. Heating Water: How much heat is required to raise the temperature of 250 g of water from 20 C to 80 C? (Specific heat of water is 4.184 J/gC).

2. Identifying a Metal: A 50 g sample of an unknown metal releases 1,200 J of heat, causing its temperature to drop by 60 C. What is the specific heat capacity of the metal?

3. The Cooling Process: If 500 J of heat is removed from 25 g of aluminum (c = 0.90 J/gC) at 100 C, what is the final temperature?

4. Mass Matters: A sample of copper (c = 0.385 J/gC) absorbs 2,500 J of heat and its temperature increases by 15 C. What is the mass of the copper?

5. First Law Concept: A system performs 150 J of work on its surroundings and absorbs 400 J of heat. Calculate the change in internal energy (delta U).

Answer Key

1. 62,760 J

2. 0.40 J/gC

3. 77.8 C

4. 432.9 g

5. +250 J

Chemistry - The Ideal Gas Law and Stoichiometry

Understanding the Relationship

Gas stoichiometry combines the principles of chemical reactions with the properties of gases. In high school chemistry, you have already learned how to use the Ideal Gas Law (PV = nRT) to find properties of a single gas. Stoichiometry allows you to use the balanced chemical equation to relate the amount of one substance to another. When these two concepts meet, you can calculate the volume of a gas produced in a reaction or determine how much of a solid reactant is needed to produce a specific pressure of gas.

The key link between these two worlds is the mole (n). Stoichiometry uses mole ratios from balanced equations, and the Ideal Gas Law solves for moles based on pressure (P), volume (V), and temperature (T).

The Ideal Gas Law Formula: PV = nRT

P is Pressure (commonly in atm or kPa)

V is Volume (must be in Liters)

n is Number of Moles

R is the Ideal Gas Constant (0.0821 L atm / mol K or 8.314 L kPa / mol K)

T is Temperature (must be in Kelvin; K = Celsius + 273)

Steps for Gas Stoichiometry Problems

1. Write or check the balanced chemical equation.

2. Identify the given information. Is it gas data (P, V, T) or mass/mole data?

3. Convert your "Given" to Moles. If you start with gas data, use n = PV / RT. If you start with mass, use the molar mass.

4. Use the Mole Ratio from the balanced equation to find the moles of the "Unknown" substance. 

5. Convert the Moles of the Unknown to the final units requested (Volume, Mass, or Pressure).

Practice Problems

1. The combustion of propane follows the equation: C3H8 + 5 O2 --> 3 CO2 + 4 H2O. If 5.00 grams of propane (C3H8) is burned, what volume of CO2 gas will be produced at 1.00 atm and 298 K?

2. Solid calcium carbonate decomposes into calcium oxide and carbon dioxide gas: CaCO3 --> CaO + CO2.  How many grams of CaCO3 are needed to produce 15.0 L of CO2 at a pressure of 105 kPa and a temperature of 300 K?

3. Hydrogen gas is produced by reacting zinc with sulfuric acid: Zn + H2SO4 --> ZnSO4 + H2. If 12.0 grams of zinc react completely, what will be the pressure of the hydrogen gas if it is collected in a 4.00 L flask at 27 degrees Celsius?

4. In the reaction 2 NaN3 --> 2 Na + 3 N2, used in car airbags, how many grams of NaN3 are required to provide 65.0 L of nitrogen gas at 1.15 atm and 30 degrees Celsius?

5. Ammonia is produced via the Haber process: N2 + 3 H2 --> 2 NH3. If 20.0 L of nitrogen gas at 200 kPa and 500 K reacts with excess hydrogen, how many moles of ammonia are produced?

Answer Key

1. 8.32 L of CO2

   Steps: Convert 5.00g C3H8 to moles (0.113 mol). Use 3:1 ratio to get 0.339 mol CO2. Use V = nRT/P.

2. 63.2 grams of CaCO3

   Steps: Use n = PV/RT to find moles of CO2 (0.631 mol). Use 1:1 ratio to find moles of CaCO3. Multiply by molar mass (100.09 g/mol).

3. 1.13 atm

   Steps: Convert 12.0g Zn to moles (0.184 mol). Use 1:1 ratio to get 0.184 mol H2. Use P = nRT/V with T=300K.

4. 130.5 grams of NaN3

   Steps: Use n = PV/RT to find moles of N2 (3.01 mol). Use 2:3 ratio to find moles of NaN3 (2.007 mol). Multiply by molar mass (65.01 g/mol).

5. 1.93 moles of NH3

   Steps: Use n = PV/RT to find moles of N2 (0.963 mol). Use 2:1 mole ratio to find moles of NH3.