Butane gas, C4 H10, is sold to campers as bottled fuel. Its...

Butane gas, $\mathrm{C}_{4} \mathrm{H}_{10}$, is sold to campers as bottled fuel. Its density at $25^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ is $2.38 \mathrm{~g} / \mathrm{L}$. What volume of butane gas at $25^{\circ} \mathrm{C}$ and 1.00 atm is required to heat one gallon of water $(d=1.00 \mathrm{~g} / \mathrm{mL})$ from $25^{\circ} \mathrm{C}$ to $98^{\circ} \mathrm{C} ?$ The reaction for the combustion of butane $\left(\Delta H_{\mathrm{f}}^{\circ}=-125.6 \mathrm{~kJ} / \mathrm{mol}\right)$ is $$ \mathrm{C}_{4} \mathrm{H}_{10}(g)+\frac{13}{2} \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+5 \mathrm{H}_{2} \mathrm{O}(g) $$

Butane gas, $\mathrm{C}_{4} \mathrm{H}_{10}$, is sold to campers as bottled fuel. Its density at $25^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ is $2.38 \mathrm{~g} / \mathrm{L}$. What volume of butane gas at $25^{\circ} \mathrm{C}$ and 1.00 atm is required to heat one gallon of water $(d=1.00 \mathrm{~g} / \mathrm{mL})$ from $25^{\circ} \mathrm{C}$ to $98^{\circ} \mathrm{C} ?$ The reaction for the combustion of butane $\left(\Delta H_{\mathrm{f}}^{\circ}=-125.6 \mathrm{~kJ} / \mathrm{mol}\right)$ is
$$
\mathrm{C}_{4} \mathrm{H}_{10}(g)+\frac{13}{2} \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+5 \mathrm{H}_{2} \mathrm{O}(g)
$$

Key Concepts

Heat Transfer and Calorimetry

This concept involves calculating the amount of energy required to change the temperature of a substance, typically using the formula Q = m·c·?T, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ?T is the temperature change. It is essential in determining the energy needed to heat water or other materials.

Combustion Reaction Enthalpy

This key concept relates to the energy release or absorption associated with a chemical reaction, specifically combustion. The enthalpy of combustion indicates how much energy is released per mole of fuel burned, allowing one to link the energy produced from a fuel source to a practical application like heating.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves using the balanced chemical equation to calculate the number of moles of reactants needed or products formed, which is critical for determining how much fuel is required to produce a specific amount of energy.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, connects the pressure, volume, temperature, and number of moles of a gas. This concept is used to convert between the amount of gas (in moles) and its volume at given conditions, making it possible to calculate the volume of gas needed at a set temperature and pressure.

Unit Conversions and Density

Understanding unit conversions is crucial for correctly applying formulas across different measurement systems, such as converting gallons to liters or grams to moles. Density, defined as mass per unit volume, is used to relate a substance's volume to its mass, which is often a necessary step in chemical calculations.

Transcript

00:01 Okay, so we're talking about butane in this problem.

00:04 So let's start with our balanced equation, which is given to us.

00:08 Okay, so we're going to go ahead and use that balance equation to find the heat of reaction.

00:16 Okay, and that's just the sum of all the heats of formation of your products, minus the sum of all your heats of formation of your reactants.

00:29 Okay, so we'll use our table of heats of formation.

00:32 So we're going to start with one of our products is co2, so there's four of them.

00:38 So four times minus 393 .5 plus five times our water vapor, which is minus 241 .8.

00:49 Be sure you use water vapor and not water.

00:52 Now we're going to subtract the butane, which is negative 125 .6.

00:58 And we're going to subtract the oxygen, but since it's an element, it's going to be zero.

01:04 So if we do all this out, we'll get minus 2657 .4 kilojoules.

01:12 So that's the amount of kilojoules released for the reaction as written.

01:17 We want to figure out how much of our butane or gasoline we need to heat up a gallon of water.

01:23 Okay, so why don't we start by putting a gallon into some units that we can work with? okay, so one gallon.

01:31 And we go ahead and change gallons to liters.

01:36 And then i'm going to change liters to milliliters so that we can use a density because we have the density of water, of course, is one.

01:47 There's 1 ,000 milliliters in a liter, and there are 3 .785 liters in one gallon.

01:56 So this is going to be 3 ,785 grams of 1 gallon.

02:03 Water.

02:06 So let's see how much energy it takes, heat that up.

02:09 So we'll start with q is minus mc delta t.

02:15 The water is what's changing temperature...

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