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By the end of this section, you will be able to:
  • Write equations representing changes in concentration and pressure for chemical species in equilibrium systems
  • Use algebra to perform various types of equilibrium calculations

We know that at equilibrium, the value of the reaction quotient of any reaction is equal to its equilibrium constant. Thus, we can use the mathematical expression for Q to determine a number of quantities associated with a reaction at equilibrium or approaching equilibrium. While we have learned to identify in which direction a reaction will shift to reach equilibrium, we want to extend that understanding to quantitative calculations. We do so by evaluating the ways that the concentrations of products and reactants change as a reaction approaches equilibrium, keeping in mind the stoichiometric ratios of the reaction. This algebraic approach to equilibrium calculations will be explored in this section.

Changes in concentrations or pressures of reactants and products occur as a reaction system approaches equilibrium. In this section we will see that we can relate these changes to each other using the coefficients in the balanced chemical equation describing the system. We use the decomposition of ammonia as an example.

On heating, ammonia reversibly decomposes into nitrogen and hydrogen according to this equation:

2 NH 3 ( g ) N 2 ( g ) + 3 H 2 ( g )

If a sample of ammonia decomposes in a closed system and the concentration of N 2 increases by 0.11 M , the change in the N 2 concentration, Δ[N 2 ], the final concentration minus the initial concentration, is 0.11 M . The change is positive because the concentration of N 2 increases.

The change in the H 2 concentration, Δ[H 2 ], is also positive—the concentration of H 2 increases as ammonia decomposes. The chemical equation tells us that the change in the concentration of H 2 is three times the change in the concentration of N 2 because for each mole of N 2 produced, 3 moles of H 2 are produced.

Δ [ H 2 ] = 3 × Δ [ N 2 ]
= 3 × ( 0.11 M ) = 0.33 M

The change in concentration of NH 3 , Δ[NH 3 ], is twice that of Δ[N 2 ]; the equation indicates that 2 moles of NH 3 must decompose for each mole of N 2 formed. However, the change in the NH 3 concentration is negative because the concentration of ammonia decreases as it decomposes.

Δ [ NH 3 ] = −2 × Δ [ N 2 ] = −2 × ( 0.11 M ) = −0.22 M

We can relate these relationships directly to the coefficients in the equation

2 NH 3 ( g ) N 2 ( g ) + 3 H 2 ( g ) Δ [ NH 3 ] = −2 × Δ [ N 2 ] Δ [ N 2 ] = 0.11 M Δ [ H 2 ] = 3 × Δ [ N 2 ]

Note that all the changes on one side of the arrows are of the same sign and that all the changes on the other side of the arrows are of the opposite sign.

If we did not know the magnitude of the change in the concentration of N 2 , we could represent it by the symbol x .

Δ [ N 2 ] = x

The changes in the other concentrations would then be represented as:

Δ [ H 2 ] = 3 × Δ [ N 2 ] = 3 x
Δ [ NH 3 ] = −2 × Δ [ N 2 ] = −2 x

The coefficients in the Δ terms are identical to those in the balanced equation for the reaction.

2 NH 3 ( g ) N 2 ( g ) + 3 H 2 ( g ) −2 x x 3 x

The simplest way for us to find the coefficients for the concentration changes in any reaction is to use the coefficients in the balanced chemical equation. The sign of the coefficient is positive when the concentration increases; it is negative when the concentration decreases.

Questions & Answers

why the elements of group 7 are called Noble gases
isaac Reply
they aren't. group 8 is the noble gasses. they are snobs that don't mix with others like nobles, they have full valence shells so they don't form bonds with other elements easily. nobles don't mingle with the common folk...
Jessica
the group 7elements are not the noble gases . according to modern periodic group 18 are called noble gases elements because their valence shell are completely field so that they can't gain or loss electron so they are not able to involve in any chemical reaction.
Leena
what is chemistry
Daniel Reply
chemistry is the branch of science which deal with the composition of matter
SHEDRACK
discuss the orbital stracture of the following methane,ethane,ethylene,acetylene
khadija Reply
Why phosphurs in solid state have one atom but in gas state have four atoms
Shehab Reply
Are nuclear reactions both exothermic reactions and endothermic reactions or what?
Blessed Reply
to what volume must 8.32 NaOH be diluted to its analytical concentration 0.20 M
Sheriza Reply
weight in mg 1.76 mole of I
Sheriza
the types of hydrocarbons
Ohanaka Reply
u are mad go and open textbook
Emmanuel
hahahahahahahahahahahahaha
Jessica
aliphatic and aromatic hydrocarbons
Osakue
stupid boy Emmanuel
Ohanaka
saturated and unsaturated
Leena
I don't use to see the messages
Adazion Reply
how can you determine the electronegativity of a compound or in molecules
Shalom Reply
when u move from left to right in a periodic table the negativity increases
reeza
Are you trying to say that the elctronegativity increases down the group and decreases across the period?
Ohanaka
yes and also increases across the period
reeza
for instance when you look at one group of elements in a periodic table electronegativity decreases when you go across the table electronegativity increases. hydrogen is more electronegative than sodium, potassium of that group. oxygen is more electronegative than carbon.
reeza
i hope we all know that organic compounds have carbon as their back bone
Madueke
OK,Thank you so much for the answer. I am happy now
Adazion Reply
can I ask you a question now
Osakue
yes
hanna
what is the oxidation number of nitrogen, oxygen and sulphur
Osakue
5, -2 & -2
hanna
What is an atom?
Adazion Reply
is a smallest particle of a chemical element that can exist
Osakue
can I ask a question
Osakue
it is a substance that cannot be broken down into simpler units by any chemical reaction
Madueke
An atom is the smallest part of an element dat can take part in chemical reaction.
Idris
an atom is the smallest part of an element that can take part in a chemical reaction nd still retain it chemical properties
Precious
Is the smallest particles of an element that take part in chemical reaction without been change
John
what are the branches of an atomic mass
Adazion Reply
Still waiting for answers for a very long time now
Adazion
Please May una reply me ooo
Adazion
that question is very strong oooo
Osakue
most of the questions I asked wasn't answered what's the problem guys?
Adazion Reply
hi, there is no problems ooo
Osakue
between H2SO4 and HCL which is the strongest dehydrating agent ?
Ibirogba
HCl is the strongest dehydrating agent
Osakue
ᴡʜᴀᴛ ᴡɪʟʟ ᴏʙsᴇʀᴠᴇᴅ ɪғ ʟᴇᴀᴅ(ɪɪ)ɴɪᴛʀᴀᴛᴇs ɪs ᴀᴅᴅᴇᴅ ᴏɴ ᴛᴏ sᴏᴅɪᴜᴍ ɪᴏᴅɪᴅᴇ sᴏʟᴜᴛɪᴏɴ
Gawaar Reply
what is the functional group of alkanals
Frankyx Reply
can someone explain salt analysis properly
Frankyx

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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