what mass of iron must react to produce 3600 kj of energy

Affiliate 7. Energy and Chemistry

Stoichiometry Calculations Using Enthalpy

Perform stoichiometry calculations using energy changes from thermochemical equations.

In Chapter 5 "Stoichiometry and the Mole", we related quantities of one substance to another in a chemic equation past performing calculations that used the balanced chemical equation; the counterbalanced chemical equation provided equivalences that we used to construct conversion factors. For case, find the following balanced chemical equation:

$\ce{2H2(g)}+\ce{O2(g)}\rightarrow \ce{2H2O(\ell)}$

In this equation, we recognize the following equivalences:

$2\text{ mol }\ce{H2}\Leftrightarrow 1\text{ mol }\ce{O2}\Leftrightarrow 2\text{ mol }\ce{H2O}$

Where ⇔ is the mathematical symbol for "is equivalent to." In our thermochemical equation, all the same, we take some other quantity — energy alter:

$\ce{2H2(g)}+\ce{O2(g)}\rightarrow \ce{2H2O(\ell)} \hspace{10mm}\Delta H =-570\text{ kJ}$

This new quantity allows u.s. to add some other equivalence to our list:

$2\text{ mol }\ce{H2}\Leftrightarrow 1\text{ mol }\ce{O2}\Leftrightarrow 2\text{ mol }\ce{H2O} \Leftrightarrow -570\text{ kJ}$

That is, nosotros tin can now add an energy amount to the equivalences — the enthalpy modify of a balanced chemical reaction. This equivalence tin as well be used to construct conversion factors so that we tin can relate enthalpy change to amounts of substances reacted or produced.

Annotation that these equivalences address a business organisation. When an amount of free energy is listed for a balanced chemical reaction, what amount(s) of reactants or products does it refer to? The answer is that relates to the number of moles of the substance equally indicated by its coefficient in the balanced chemical reaction. Thus, ii mol of H₂ are related to −570 kJ, while ane mol of O₂ is related to −570 kJ. This is why the unit of measurement on the energy change is kJ, not kJ/mol.

For instance, consider the following thermochemical equation:

$\ce{H2(g)}+\ce{Cl2(g)}\rightarrow \ce{2HCl(g)}\hspace{10mm}\Delta H = -184.6\text{ kJ}$

The equivalences for this thermochemical equation are:

$1\text{ mol }\ce{H2}\Leftrightarrow 1\text{ mol }\ce{Cl2} \Leftrightarrow 2\text{ mol }\ce{HCl}\Leftrightarrow -184.6\text{ kJ}$

Suppose we asked how much energy is given off when 8.22 mol of H_two react. We would construct a conversion gene betwixt the number of moles of H₂ and the energy given off, −184.6 kJ:

$8.22\text{ }\cancel{\text{mol }\ce{H2}}\times \dfrac{-184.6\text{ kJ}}{1\text{ }\cancel{\text{mol }\ce{H2}}}=-1,520\text{ kJ}$

The negative sign means that this much free energy is given off.

Problem

Determine how much free energy is given off when 222.4 grand of North₂ reacts in the following thermochemical equation:

$\ce{N2(g)}+\ce{3H2(g)}\rightarrow \ce{2NH3(g)}\hspace{10 mm}\Delta H=-91.8\text{ kJ}$

Solution

The counterbalanced thermochemical equation relates the energy modify to moles, not grams, then nosotros first convert the amount of N₂ to moles and then use the thermochemical equation to determine the energy change:

$222.4\text{ }\cancel{\text{g }\ce{N2}}\times\dfrac{1\text{ }\cancel{\text{mol }\ce{N2}}}{28.00\text{ }\cancel{\text{g }\ce{N2}}}\times\dfrac{-91.8\text{ kJ}}{1\text{ }\cancel{\text{mol }\ce{N2}}}=-729\text{ kJ}$

Examination Yourself

Determine how much oestrus is given off when one.00 g of H_ii reacts in the following thermochemical equation:

$\ce{N2(g)}+\ce{3H2(g)}\rightarrow \ce{2NH3(g)}\hspace{10 mm}\Delta H=-91.8\text{ kJ}$

Respond

−xv.i kJ

Like whatever stoichiometric quantity, we can start with energy and determine an amount, rather than the other fashion around.

Problem

Determine what mass of NO can be made if 558 kJ of free energy are supplied, given the following thermochemical equation:

$\ce{N2(g)}+\ce{O2(g)}\rightarrow \ce{2NO(g)}\hspace{10 mm}\Delta H=180.6\text{ kJ}$

Solution

This time, we kickoff with an amount of free energy:

$558\text{ \cancel{kJ}}\times \dfrac{2 \text{ \cancel{mol NO}}}{180.6\text{ \cancel{kJ}}}\times \dfrac{30.0\text{ g NO}}{1\text{ \cancel{mol NO}}}=185\text{ g NO}$

Exam Yourself

Given the following equation, how many grams of N₂ will react if 100.0 kJ of energy are supplied?

$\ce{N2(g)}+\ce{O2(g)}\rightarrow \ce{2NO(g)}\hspace{10mm}\Delta H=180.6\text{ kJ}$

Reply

15.5 k

Chemistry Is Everywhere: Welding with Chemical Reactions

One very energetic reaction is called the thermite reaction. Its classic reactants are aluminum metallic and iron(III) oxide; the reaction produces iron metallic and aluminum oxide:

$\ce{2Al(s)}+\ce{Fe2O3(s)}\rightarrow\ce{Al2O3(s)}+\ce{2Fe(s)}\hspace{10 mm}\Delta H=-850.2\text{ kJ}$

When properly done, the reaction gives off so much energy that the iron product comes off equally a liquid. (Iron usually melts at 1,536°C.) If carefully directed, the liquid iron can fill spaces between ii or more than metal parts and, after it quickly cools, can weld the metallic parts together.

Thermite reactions are used for this purpose fifty-fifty today. For civilian purposes, they are used to re-weld broken locomotive axles that cannot be easily removed for repair. They are used to weld railroad tracks together. Thermite reactions tin can also be used to separate thin pieces of metal if, for whatever reason, a torch doesn't work.

A clay pot with flames and smoke coming out of it sitting on railway tracks. — Figure 7.2 "Thermite Reaction." A small clay pot contains a thermite mixture. Information technology is reacting at loftier temperature in the photo and will somewhen produce molten metallic to join the railroad tracks beneath information technology.

Thermite reactions are also used for military purposes. Thermite mixtures are oftentimes used with additional components as incendiary devices — devices that start fires. Thermite reactions are also useful in disabling enemy weapons: a slice of arms doesn't work so well when information technology has a hole melted into its barrel because of a thermite reaction!

The free energy change of a chemical reaction can exist used in stoichiometry calculations.

Questions

Write the equivalences that this balanced thermochemical equation implies:
$\ce{PCl3(g)}+\ce{Cl2(g)}\rightarrow\ce{PCl5(g)}\quad\Delta H=-87.9\text{ kJ}$
Write the equivalences that this balanced thermochemical equation implies:
$\ce{2SO3(g)}\rightarrow \ce{2SO2(g)}+\ce{O2(g)}\quad\Delta H=197.9\text{ kJ}$
How many kilojoules are given off when 17.eight mol of CH_four(yard) react in the post-obit equation?
$\ce{CH4(g)}+\ce{2O2(g)}\rightarrow \ce{CO2(g)}+\ce{2H2O(\ell)}\quad\Delta H=-890.1\text{ kJ}$
How many kilojoules are captivated when 0.772 mol of N₂(grand) reacts in the post-obit equation?
$\ce{N2(g)}+\ce{2NO(g)}\rightarrow \ce{2N2O(g)}\quad\Delta H=73.8\text{ kJ}$
How many kilojoules are absorbed when 23.09 mol of C_sixH_half-dozen(ℓ) are formed in the following equation?
$\ce{6C(s)}+\ce{3H2(g)}\rightarrow \ce{C6H6(\ell)}\quad\Delta H=49.0\text{ kJ}$
How many kilojoules are given off when 8.32 mol of Mg react in the following equation?
$\ce{2Mg(s)}+\ce{O2(g)}\rightarrow \ce{2MgO(s)}\quad\Delta H=-1,213\text{ kJ}$
Glucose (C₆H₁₂O₆) is the main fuel metabolized in animal cells. How much energy is given off when 100.0 g of C₆H₁₂O₆ react in the following equation?
$\ce{C6H12O6}+\ce{6O2}\rightarrow\ce{6CO2}+\ce{6H2O}\quad\Delta H=-2,799\text{ kJ}$
How much energy is given off when 288 k of Fe are produced, given the post-obit thermochemical equation?
$\ce{2Al(s)}+\ce{Fe2O3(s)}\rightarrow\ce{Al2O3(s)}+\ce{2Fe(s)}\quad\Delta H=-850.2\text{ kJ}$
How much energy is absorbed when 85.two g of CO₂ are reacted in the following thermochemical equation?
$\ce{2CO2(g)}\rightarrow \ce{2CO(g)}+\ce{O2(g)}\quad\Delta H=566\text{ kJ}$
How much energy is absorbed when 55.nine thousand of Na⁺(aq) are reacted in the following thermochemical equation?
$\ce{2Na^+(aq)}+\ce{SO4^{2-}(aq)}\rightarrow\ce{Na2SO4(s)}\quad\Delta H=819.8\text{ kJ}$
NaHCO₃ decomposes when exposed to heat. What mass of NaHCO_iii is decomposed by 256 kJ, in the following thermochemical equation?
$\ce{2NaHCO3(s)}\rightarrow \ce{Na2CO3(s)}+\ce{CO2(g)}+\ce{H2O(\ell)}\quad\Delta H=91.5\text{ kJ}$
HgO decomposes when exposed to heat. What mass of O₂ tin be made with 100.0 kJ, in the post-obit thermochemical equation?
$\ce{2HgO(s)}\rightarrow \ce{2Hg(\ell)}+\ce{O2(g)}\quad\Delta H=1816\text{ kJ}$
What mass of And so₃ is needed to generate 1,566 kJ in the following thermochemical equation?
$\ce{Fe2O3(s)}+\ce{3SO3(g)}\rightarrow\ce{Fe2(SO4)3(s)}\quad \Delta H = -570.2\text{ kJ}$
What mass of HBr volition exist formed when 553 kJ of energy are given off in the following thermochemical equation?
$\ce{H2(g)}+\ce{Br2(\ell)}\rightarrow \ce{2HBr(g)}\quad \Delta H=-72.6\text{ kJ}$