/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 91 Assume that \(4.19 \times 10^{6}... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 91

Assume that \(4.19 \times 10^{6} \mathrm{~kJ}\) of energy is needed to heat a home. If this energy is derived from the combustion of methane \(\left(\mathrm{CH}_{4}\right)\), what volume of methane, measured at STP, must be burned? \(\left(\Delta H_{\text {combustion }}^{\circ}\right.\) for \(\mathrm{CH}_{4}=-891 \mathrm{~kJ} / \mathrm{mol}\) )

Short Answer

Expert verified
The volume of methane required to provide the given amount of energy to heat the home is approximately 105,484.56 liters at STP.

Step by step solution

01

Calculate moles of methane needed to produce the given energy

We are given the energy needed to heat the home as 4.19 x 10^6 kJ and the enthalpy of combustion of methane as -891 kJ/mol. We will use these values to find the moles of methane needed to produce the given energy. Energy_needed = Enthalpy_of_combustion x Moles_of_methane Moles_of_methane = Energy_needed / Enthalpy_of_combustion = \( \frac{4.19 \times 10^6 \,\text{kJ}}{-891 \,\text{kJ/mol}} \)
02

Solve for moles of methane

Now we divide the energy needed by the enthalpy of combustion to find the moles of methane needed: Moles_of_methane = \( \frac{4.19 \times 10^6}{-891} \) Moles_of_methane 鈮� 4702.47 mol
03

Use the ideal gas law to find the volume of methane

Now, we have the moles of methane needed. We will use the ideal gas law, PV=nRT, to find the volume of methane at STP (Standard Temperature and Pressure). At STP, T = 273.15 K and P = 1 atm (1 atm = 101325 Pa). R (universal gas constant) = 8.314 J/(mol*K) Since pressure is given in atm, we will use R in L*atm/mol*K which is equal to 0.0821 L*atm/mol*K. Now we can solve for the volume of methane using the ideal gas law, PV=nRT: V = \( \frac{nRT}{P} \) V = \( \frac{4702.47 \, \text{mol} \times 0.0821\, \text{L*atm/mol*K} \times 273.15\, \text{K}}{1 \, \text{atm}} \)
04

Solve for the volume of methane

Now we can calculate the volume of methane required: V 鈮� \( \frac{4702.47 \times 0.0821 \times 273.15}{1} \) V 鈮� 105484.56 L The volume of methane required to provide the given amount of energy to heat the home is approximately 105,484.56 liters at STP.

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Most popular questions from this chapter

Given the following data $$ \begin{array}{ll} \mathrm{NH}_{3}(g) \longrightarrow \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) & \Delta H=46 \mathrm{~kJ} \\ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) & \Delta H=-484 \mathrm{~kJ} \end{array} $$ calculate \(\Delta H\) for the reaction $$ 2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{O}_{2}(g)+4 \mathrm{NH}_{3}(g) $$ On the basis of the enthalpy change, is this a useful reaction for the synthesis of ammonia?

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is \(40 . \mathrm{cm}^{3} .\) If the combustion of this mixture releases 950. J of energy, to what volume will the gases expand against a constant pressure of 650 . torr if all the energy of combustion is converted into work to push back the piston?

It has been determined that the body can generate \(5500 \mathrm{~kJ}\) of energy during one hour of strenuous exercise. Perspiration is the body's mechanism for eliminating this heat. What mass of water would have to be evaporated through perspiration to rid the body of the heat generated during two hours of exercise? (The heat of vaporization of water is \(40.6 \mathrm{~kJ} / \mathrm{mol}\).)

Consider the following cyclic process carried out in two steps on a gas: Step 1: \(45 \mathrm{~J}\) of heat is added to the gas, and \(10 . \mathrm{J}\) of expansion work is performed. Step 2: \(60 . \mathrm{J}\) of heat is removed from the gas as the gas is compressed back to the initial state. Calculate the work for the gas compression in step \(2 .\)

Calculate the internal energy change for each of the following. a. One hundred (100.) joules of work is required to compress a gas. At the same time, the gas releases \(23 \mathrm{~J}\) of heat. b. A piston is compressed from a volume of \(8.30 \mathrm{~L}\) to \(2.80 \mathrm{~L}\) against a constant pressure of \(1.90 \mathrm{~atm} .\) In the process, there is a heat gain by the system of \(350 . \mathrm{J}\). c. A piston expands against \(1.00 \mathrm{~atm}\) of pressure from \(11.2 \mathrm{~L}\) to \(29.1 \mathrm{~L}\). In the process, \(1037 \mathrm{~J}\) of heat is absorbed.
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