On a cold day, you can warm your hands with a "heat pad," a...

On a cold day, you can warm your hands with a "heat pad," a device that uses the oxidation of iron to produce energy as heat. $$ 4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s}) $$ (IMAGE CANNOT COPY) What mass of iron is needed to supply the energy required to warm $15 \mathrm{mL}$ of water $(d=1.00 \mathrm{g} / \mathrm{mL})$ from $23^{\circ} \mathrm{C}$ to $37^{\circ} \mathrm{C} ?$

On a cold day, you can warm your hands with a "heat pad," a device that uses the oxidation of iron to produce energy as heat.
$$
4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})
$$
(IMAGE CANNOT COPY)
What mass of iron is needed to supply the energy required to warm $15 \mathrm{mL}$ of water $(d=1.00 \mathrm{g} / \mathrm{mL})$ from $23^{\circ} \mathrm{C}$ to $37^{\circ} \mathrm{C} ?$

Key Concepts

Calorimetry

Calorimetry is the study of measuring heat transfer in physical and chemical processes. In this context, it involves calculating the amount of heat required to raise the temperature of a substance—in this case, water—using the relationship q = m × C × ?T, where m represents mass, C the specific heat capacity, and ?T the change in temperature.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates how much heat energy is required to raise one gram of the substance by one degree Celsius. For water, which has a high specific heat capacity, this value is crucial for determining the energy needed to achieve a given temperature change.

Stoichiometry

Stoichiometry involves using the molar relationships in a balanced chemical equation to connect quantities of reactants and products. In this problem, it is used to relate the amount of iron oxidized in the exothermic reaction to the heat energy released, which in turn is used to warm water.

Exothermic Reactions

Exothermic reactions are chemical reactions that release energy, usually in the form of heat. The oxidation of iron is an example of an exothermic reaction, where the energy released by the formation of iron(III) oxide can be harnessed to warm water.

Reaction Enthalpy

Reaction enthalpy (or heat of reaction) quantifies the total heat released or absorbed during a chemical reaction under constant pressure. For the oxidation of iron, knowing the reaction enthalpy allows one to calculate the amount of energy produced per mole of iron reacted, which is essential for determining the mass of iron needed for a specific energy output.

Transcript

00:01 Okay, so for this question, the first thing that we can do is convert the 15 milliliters of water into grams.

00:08 So we have 15 millimeters of water and they tell us the density is 1 gram per milliliter.

00:14 At 1 gram per millimeter, the milliliters will cancel out and we're left with grams and we get 15 grams of water.

00:21 Now the next thing that we can do is calculate the change in temperature.

00:26 So we have the initial temperature as 23 degrees celsius and the final temperature as 37 degrees celsius right so in order to convert celsius in the kelvin we just got to add 273 to it and we should get to 296 kelvin and 310 kelvin now let's calculate delta t so delta t is the t final it final minus t initial right, t final is 310 kelvin and t initial is 296 kelvin.

01:09 And we get delta t to be equal to 14 kelvin.

01:13 Now the next thing that we can do is we can calculate how much energy is needed to raise 15 grams of water 14 by 14 degrees kelvin.

01:23 So we need to know that the c of water is 4 .184 joules per gram times kelvin.

01:29 This is a constant.

01:30 You can look this up in the textbook.

01:32 So the equation we need to use is q is equal to m c delta t right so m is the mass and we have 15 grams c is 4 .184 joules per gram times kelvin and delta t right we calculated here is 14 kelvin so kelvin cancels out grams cancels out or less than joules as units and we get the answer to be 878 .64 joules.

02:03 Now the next thing that we can do is calculate the delta h of this reaction right here right so in order to calculate the delta h of a reaction all we got to do is take the sum of the delta h on the product side product and we subtract it from the sum of the delta h on the reactant side okay so on the product side we have fe 203 we have two moles of it right so we have two moles of fe203.

02:43 Actually, since we only have one on this side, we only need one parentheses.

02:47 Okay, so we have two moles, and we know the delta h of fe203 is negative h25 .5 kilojoules...

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