How much heat is needed to warm 50.0 g of water from 20.0 °C to 30.0 °C? The specific heat of water is 4.184 J/(g·°C). Give the answer to three significant figures.
2.09 kJ
✓
0.209 kJ
20.9 kJ
6.28 kJ
Correct Answer
2.09 kJ
Using q = m × c × ΔT gives 50.0 g × 4.184 J/(g·°C) × 10.0 °C = 2092 J, which is 2.09 kJ. The value 0.209 kJ comes from shifting the decimal one place too far when converting joules to kilojoules. The value 20.9 kJ is the same decimal slip in the other direction. The value 6.28 kJ results from using the final temperature of 30.0 °C in place of the temperature change.
Category: Specific Heat Calculations
Question 2
A 25.0 g sample of water cools from 40.0 °C to 30.0 °C. Using a specific heat of 4.184 J/(g·°C), what is q for the water, to three significant figures?
+1.05 kJ
-1.05 kJ
✓
-4.18 kJ
-3.14 kJ
Correct Answer
-1.05 kJ
The temperature change is final minus initial, 30.0 °C - 40.0 °C = -10.0 °C, so q = 25.0 g × 4.184 J/(g·°C) × (-10.0 °C) = -1046 J, or -1.05 kJ. The negative sign shows the water lost heat. The value +1.05 kJ has the right size but the wrong sign for a cooling sample. The value -4.18 kJ uses the initial temperature of 40.0 °C as if it were the change. The value -3.14 kJ uses the final temperature of 30.0 °C as if it were the change.
Category: Specific Heat Calculations
Question 3
The energy stored in the chemical bonds of gasoline, waiting to be released when the fuel burns, is classified as which type of energy?
Kinetic energy
Thermal energy
Potential energy
✓
Radiant energy
Correct Answer
Potential energy
Chemical energy is a form of potential energy, energy held because of the arrangement and attractions of atoms and electrons, and it is released when bonds rearrange during combustion. Kinetic energy is the energy of motion, while the energy described here is held in the arrangement of atoms in the bonds, not in their motion. Thermal energy is the kinetic energy of randomly moving particles, which is what burning produces rather than what is stored. Radiant energy is energy carried by light.
Category: Energy Forms and Units
Question 4
A reaction run in a beaker makes the outside of the beaker feel warm. How is the reaction classified, and what is the sign of q for the reaction itself?
Endothermic, with q positive
Exothermic, with q positive
Endothermic, with q negative
Exothermic, with q negative
✓
Correct Answer
Exothermic, with q negative
Heat flowing out of the reacting system into the beaker and your hand means the system lost energy, so the process is exothermic and q for the system is negative. Endothermic, with q positive describes a reaction that absorbs heat and makes its container feel cold. Exothermic, with q positive pairs the right label with the wrong sign. Endothermic, with q negative is a contradictory combination, since an endothermic system gains heat.
Category: Heat Flow and Sign Conventions
Question 5
Equal masses of four substances each absorb the same amount of heat. Which substance shows the largest temperature increase?
Copper, 0.385 J/(g·°C)
✓
Water, 4.184 J/(g·°C)
Aluminum, 0.897 J/(g·°C)
Iron, 0.449 J/(g·°C)
Correct Answer
Copper, 0.385 J/(g·°C)
Rearranging q = m × c × ΔT gives ΔT = q / (m × c), so with the same heat and mass, the substance with the smallest specific heat warms the most. Copper, 0.385 J/(g·°C), has the smallest value. Water, 4.184 J/(g·°C), has the largest value and would warm the least. Aluminum, 0.897 J/(g·°C), and iron, 0.449 J/(g·°C), both have larger specific heats than copper and would warm less.
Category: Specific Heat Calculations
Question 6
What is the name for the amount of heat needed to raise the temperature of an entire object, such as a whole iron skillet, by 1 °C?
Specific heat
Heat capacity
✓
Molar enthalpy
Thermal equilibrium
Correct Answer
Heat capacity
Heat capacity describes a whole object, so it depends on how much matter the object contains: a large skillet has a larger heat capacity than a small one made of the same iron. Specific heat is the heat needed per gram of a substance, not per object. Molar enthalpy is an enthalpy change expressed per mole. Thermal equilibrium is the condition of two objects at the same temperature with no net heat flow.
Category: Energy Forms and Units
Question 7
A 50.0 g metal sample at 100.0 °C is placed in 100.0 g of water at 20.0 °C. The final temperature of both is 25.0 °C. Assuming no heat is lost and using 4.184 J/(g·°C) for water, what is the specific heat of the metal to three significant figures?
0.523 J/(g·°C)
0.279 J/(g·°C)
0.558 J/(g·°C)
✓
1.12 J/(g·°C)
Correct Answer
0.558 J/(g·°C)
The water gains 100.0 g × 4.184 J/(g·°C) × 5.0 °C = 2092 J, and the metal loses the same amount over a 75.0 °C drop, so c = 2092 J / (50.0 g × 75.0 °C) = 0.558 J/(g·°C). The value 0.523 J/(g·°C) comes from using 80.0 °C, the difference between the two starting temperatures, as the metal's temperature change. The value 0.279 J/(g·°C) uses the water's mass in place of the metal's. The value 1.12 J/(g·°C) uses only half the metal's mass.
Category: Calorimetry
Question 8
In a bomb calorimeter, the sample reacts inside a sealed, rigid steel vessel. Under which condition does the reaction take place?
Constant pressure
Constant temperature
Open to the atmosphere
Constant volume
✓
Correct Answer
Constant volume
The rigid sealed vessel cannot change size, so the reaction occurs at constant volume, which makes bomb calorimeters well suited to combustion reactions that produce gases. Constant pressure describes a coffee-cup calorimeter open to the air. Constant temperature is not the condition, because the measurement depends on the temperature rising. Open to the atmosphere is the opposite of a sealed vessel.
Category: Calorimetry
Question 9
A snack label lists 150 Calories (food Calories, each equal to 1 kcal). Using 1 kcal = 4.184 kJ, how many kilojoules is this, to three significant figures?
628 kJ
✓
35.9 kJ
0.628 kJ
150 kJ
Correct Answer
628 kJ
A food Calorie is a kilocalorie, so 150 kcal × 4.184 kJ/kcal = 627.6 kJ, which rounds to 628 kJ. The value 35.9 kJ comes from dividing by 4.184 instead of multiplying. The value 0.628 kJ treats the food Calorie as a small calorie, losing a factor of 1000. The value 150 kJ wrongly assumes a Calorie and a kilojoule are the same size.
Category: Energy Forms and Units
Question 10
A gas absorbs 250 J of heat from its surroundings and, while expanding, does 100 J of work on the surroundings. What is the change in its internal energy, ΔU?
+350 J
+150 J
✓
-150 J
-350 J
Correct Answer
+150 J
By the first law, ΔU = q + w. Heat absorbed is positive (q = +250 J) and work done by the system is negative (w = -100 J), so ΔU = +150 J. The value +350 J treats the work done by the gas as energy gained. The value -150 J reverses both signs. The value -350 J adds the two amounts and gives the total a negative sign.
Category: First Law and State Functions
Question 11
Which pair consists of two quantities whose values depend on the path taken between the initial and final states of a system?
Enthalpy and internal energy
Enthalpy and heat
Heat and work
✓
Internal energy and work
Correct Answer
Heat and work
Heat and work are path dependent: the same overall change can be reached with different splits between heat transferred and work done. Enthalpy and internal energy are both state functions, fixed only by the current state. Enthalpy and heat includes enthalpy, a state function. Internal energy and work includes internal energy, a state function.
Category: First Law and State Functions
Question 12
In an insulated cup, 50.0 g of water at 80.0 °C is mixed with 150.0 g of water at 20.0 °C. Assuming no heat is lost, what is the final temperature, to three significant figures?
50.0 °C
65.0 °C
40.0 °C
35.0 °C
✓
Correct Answer
35.0 °C
Heat lost by the warm water equals heat gained by the cool water: 50.0(80.0 - T) = 150.0(T - 20.0), which gives 7000 = 200T and T = 35.0 °C. The result sits closer to 20.0 °C because there is three times as much cool water. The value 50.0 °C is a simple average that ignores the different masses. The value 65.0 °C weights the masses the wrong way around. The value 40.0 °C does not satisfy the heat balance.
Category: Calorimetry
Question 13
For 1/2 N2(g) + 3/2 H2(g) → NH3(g), ΔH = -46 kJ. What is ΔH for 2 NH3(g) → N2(g) + 3 H2(g)?
+92 kJ
✓
-92 kJ
+46 kJ
-46 kJ
Correct Answer
+92 kJ
Reversing a thermochemical equation changes the sign of ΔH, and doubling the coefficients doubles its size, so ΔH = 2 × (+46 kJ) = +92 kJ. Decomposing ammonia into its elements is endothermic. The value -92 kJ doubles correctly but keeps the original sign. The value +46 kJ reverses the sign but forgets to double. The value -46 kJ makes neither change.
Category: Enthalpy and Thermochemical Equations
Question 14
Methane, CH4, releases 890 kJ of heat per mole burned. How much heat is released when 8.00 g of CH4 (molar mass 16.0 g/mol) burns completely?
890 kJ
445 kJ
✓
1780 kJ
7120 kJ
Correct Answer
445 kJ
First convert mass to moles: 8.00 g / 16.0 g/mol = 0.500 mol. Then 0.500 mol × 890 kJ/mol = 445 kJ released. The value 890 kJ is the heat for one full mole, not for the sample. The value 1780 kJ comes from dividing by 0.500 mol instead of multiplying. The value 7120 kJ multiplies the heat per mole by the mass in grams.
Category: Enthalpy and Thermochemical Equations
Question 15
Given C(s) + O2(g) → CO2(g), ΔH = -393.5 kJ, and CO(g) + 1/2 O2(g) → CO2(g), ΔH = -283.0 kJ, what is ΔH for C(s) + 1/2 O2(g) → CO(g)?
-676.5 kJ
+110.5 kJ
-110.5 kJ
✓
+676.5 kJ
Correct Answer
-110.5 kJ
Keep the first equation and reverse the second (making its ΔH +283.0 kJ). Adding them cancels CO2 and leaves C(s) + 1/2 O2(g) → CO(g), with ΔH = -393.5 kJ + 283.0 kJ = -110.5 kJ. The value -676.5 kJ adds the two equations without reversing the second. The value +110.5 kJ has the right size but the wrong sign. The value +676.5 kJ reverses the sum of both equations.
Category: Hess's Law and Formation
Question 16
A bomb calorimeter absorbs 10.0 kJ for every 1 °C rise in its temperature. Burning a sample inside it raises the temperature by 2.50 °C. How much heat did the reaction release?
4.00 kJ
12.5 kJ
0.250 kJ
25.0 kJ
✓
Correct Answer
25.0 kJ
The heat absorbed by the calorimeter is 10.0 kJ/°C × 2.50 °C = 25.0 kJ, and with no heat lost the reaction released that same amount. The value 4.00 kJ comes from dividing 10.0 by 2.50. The value 12.5 kJ adds the two numbers instead of multiplying them. The value 0.250 kJ divides the temperature change by the calibration value.
Category: Calorimetry
Question 17
Which equation is the standard formation reaction for liquid water?
H2(g) + 1/2 O2(g) → H2O(l)
✓
2 H2(g) + O2(g) → 2 H2O(l)
H2O(g) → H2O(l)
2 H(g) + O(g) → H2O(l)
Correct Answer
H2(g) + 1/2 O2(g) → H2O(l)
A formation reaction makes exactly 1 mole of the compound from its elements in their standard states, so fractional coefficients are allowed: H2(g) + 1/2 O2(g) → H2O(l). The equation 2 H2(g) + O2(g) → 2 H2O(l) makes 2 moles instead of 1. The equation H2O(g) → H2O(l) is condensation, not formation from elements. The equation 2 H(g) + O(g) → H2O(l) starts from atoms, which are not the standard states of hydrogen and oxygen.
Category: Hess's Law and Formation
Question 18
For CaCO3(s) → CaO(s) + CO2(g), use these standard enthalpies of formation: CaCO3(s) -1207 kJ/mol, CaO(s) -635 kJ/mol, CO2(g) -394 kJ/mol. What is the standard enthalpy change of the reaction?
-178 kJ
+178 kJ
✓
-2236 kJ
+2236 kJ
Correct Answer
+178 kJ
The reaction enthalpy is the sum for the products minus the sum for the reactants: (-635 + -394) - (-1207) = -1029 + 1207 = +178 kJ, so decomposing limestone is endothermic. The value -178 kJ subtracts in the wrong order (reactants minus products). The value -2236 kJ adds all three values instead of subtracting the reactant. The value +2236 kJ makes the same error with the sign flipped.
Category: Hess's Law and Formation
Question 19
Which of these everyday processes is endothermic?
Freezing water
Burning propane
Melting ice
✓
Condensing steam
Correct Answer
Melting ice
Melting ice absorbs heat from its surroundings to separate the water molecules held in the solid, so it is endothermic. Freezing water releases that same heat, so it is exothermic. Burning propane is a combustion reaction that releases heat. Condensing steam releases heat as gas molecules come together into a liquid.
Category: Heat Flow and Sign Conventions
Question 20
In thermochemistry, what does the word heat refer to?
The temperature of a hot object
Total particle energy stored in a sample
Work done by an expanding gas
Energy transferred because of a temperature difference
✓
Correct Answer
Energy transferred because of a temperature difference
Heat is energy in transit: it flows from a warmer object to a cooler one because their temperatures differ. The temperature of a hot object is a measure of how hot it is, not an amount of energy transferred. Total particle energy stored in a sample describes the energy a substance contains, not energy moving between objects. Work done by an expanding gas is a separate kind of energy transfer.
Category: Heat Flow and Sign Conventions