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A. It is required to determine the thermal value of the synthesis of CH2O, from C, H„, and O,.

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We start with 12 grams of carbon, 2 of hydrogen, and 48 of oxygen; these combine to form 18 grams of water, and 44 grams of carbon dioxide (C + H2+O ̧ = CO2+H2O). But the same quantities of carbon, hydrogen, and oxygen might be (theoretically) combined to form 46 grams of formic acid, which could then be oxidised, by 16 grams of oxygen, to form 18 grams of water and 44 grams of carbon dioxide. Stated in formulæ these changes are

(1) C+H2+O2=CH2O2;

(2) CH,O,+O=CO,+H,O. The following are the thermal values of the different portions of these changes:

but

[C, O2]=96,960+: [H2, O]=68,360+: [CH2O2, 0]= 65,900+

[C, O2]+[H2, 0]=[C, H2, O2]+[CH2O2, O]=165,320+ .. [C, H2, O2]=[C, O2]+[H2, O]-[CH202, 0]= 99,420+. B. A rather more complicated example is furnished by the determination of the thermal values of the actions (1) [H, Br], (2) [H, I]; i.e. of the reactions whereby HBr and HI are conceived to be formed from their elements.

(1) [H, Br]. The data are

[H, Cl, Aq]=39,300; [HBr, Aq]= 19,9001:

therefore assuming that

it follows that

[H, Br, Aq]=[H, Cl, Aq]

[H, Br]=39,300 — 19,900=19,400.

But is the formation of an aqueous solution of HBr from H, Br, and water attended with the same thermal change as accompanies the formation of an aqueous solution of HC1 from H, Cl, and water? Or, if this assumption is not justified by facts, what is the difference between the thermal values of the two changes?

Now, in the first place, the thermal values of the formation of KCI and KBr in aqueous solution are equal, i.e.

[KOHAq, HClAq]=[KOHAq, HBrAq].

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sign is given it is to be understood that heat is evolved.

But the replacement of Br by C1 is attended with a considerable evolution of heat; the data here are

[KBrAq, Cl]=11,500.

Now if we analyse this change we find that the thermal expression when expanded becomes

but

[K, Cl, Aq]+[Br, Aq]–[K, Br, Aq]=11,500:

[Br, Aq]=500:

.. [K, Cl, Aq]-[K, Br, Aq]=11,500-500=11,000.

That is to say, the replacement of Br by Cl in aqueous solution is represented by the thermal value 11,000 units, and as the heat of neutralisation, in aqueous solution, of KOH by HCl is equal to that of KOH by HBr, it follows that

[H, Br, Aq]=[H, Cl, Aq] - 11,000=28,300 :

and as [HBr, Aq] = 19,900, it follows that [H, Br] = 8,400. (2) [H, I]. The data are

[H, Cl, Aq]=39,300; [HI, Aq]= 19,200.

Now

[KOHAq, HIAq]=[KOHAq, HClAq] – 70 :

also

[KIAq, Cl]=26,200 (iodine separating as solid) :

.. replacement of I by Cl is accompanied by evolution of 26,200 – 70 = 26,130 units:

and as

it follows that

.. [H, I, Aq]=[H, Cl, Aq]–26,130=13,170 :

[HI, Aq]= 19,200

[H, I]= −6,030.

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C. The heat of formation of H2SO, from its elements, i.e. the thermal value of the change [H3, S, Oʻ], has been calculated by Berthelot. Thus,

(a) oxidation of sulphurous acid in aqueous solution by chlorine;

[H2SO3Aq, H2O, CI2] = 73,900:

this expression when expanded becomes,

73,900=2 [H, Cl, Aq]+[H2SO3Aq, O] - [H2O].

But

2 [H, Cl, Aq]=78,600: and [H3, 0]=68,400 :

.. [H2SO3Aq, O]=73,900 - (78,600-68,400)=63,700+ .........(1)

(b) [SO2, Aq]=7,700:

but, assuming that when SO, is dissolved in water the solution contains H2SO3, it follows that

[SO2, Aq]=[H2O, SO2, Aq] :

.. from (1) [SO2, H2O, O, Aq]=63,700+7,700=71,400+ ......(2)

(c) [S, O2]=69,000:

.. from (2) [S, O2, O, H2O, Aq]=71,400+69,900=141,300+...(3)

(d) [SO3, Aq]=37,400:

now, dividing (3) into two parts, we have

part (a)...[S, O2, 0], and part (6)...[SO3, H2O, Aq];

but we know the value of part (6), and also the total value,
..[S, 02, 0], i.e. [S, O3],141,300 - 37,400=103,900......(4)

(e) [H2SO4, Aq]=17,000:

Now we have the values,

(a) [S, O3]=103,900: (b) [SO3, H2O]=?: (c) [H2SO4, Aq]= 17,000:

(b)+(c)=37,400;

.. [SO3, H2O]=20,400.

But [S, O3]=103,900; .. [S, O3, H2O]=103,900+20,400=124,300...

but [H2, 0]=68,400:

...(5)

.. from (5) [S, O2, 0, H2, O] i.e. [S, O1, H2]= 124,300+68,400

=192,700+.

The calculation of so-called heats of formation are all based on the principle we are now discussing.

D. Thus, required the heat of formation of methane (CH). We start with the two systems (1) C + H ̧, (2) CH ̧. Each is completely oxidised to the same final products, viz. CO2+2H,O; the difference between the quantities of heat evolved in these two changes is called the heat of formation of CH1. Thus,

[C, O2]=96,900: 2 [H2, O]=136,800: sum=233,700
but [CH, O']=213,500

.. [C, H1]= 20,200+.

As it is important that a definite meaning should be attached to the expression 'heat of formation,' a few more examples are given.

E. Required the thermal value of the reaction [H, C, N], that is, of the reaction whereby HCN may be conceived to be formed from its elements.

Data; [C, O2]=96,900: [H2, O]=34,200: sum=131,100 (N is incombustible) but [CNH, §0]=159,500

.. [C, N, H]1= 28,400-.

F. Required the thermal value of the reaction [N2, O]. Data; the reaction

C+2N2O=2N2+ CO2 when expanded thermally is [C, 2N2O]=[C, O]-2 [N2, O]=133,900:

G.

Data;

but C+2N2+O2=CO2+2N2

i.e. [C, 2N, O.]=[C, O2]=96,900 :

.. 2 [N2, O]=37,000—

.. [N2, O]=18,500-.

Required the thermal value of the reaction [N, O].
CN+2NO=CO2+3N, or in thermal notation

[CN, 2NO] =[C, O2]–[C, N] − 2 [N, O]=174,600:
but CN+0=CO2+N

=[C, O3]-[C, N]=130,900:

.. 2 [N, O]=43,700 - :

.. [N, O]=21,850-.

H. Required the thermal value of the reaction

C2H2O+C2H2O2=(C2H¿)C2H2O2+H2O;

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1 The transference of N from the molecule N, to the molecule HCN is assumed

to be accompanied by no thermal change. See post par. 132.

The heat of formation of a substance will of course vary according as the substance is formed in the gaseous, liquid, or solid state, and also according to the temperature of formation. The following examples will illustrate this.

I. Required the thermal value of the formation of aldehyde from its elements, i.e. of the reaction [C2, Hʻ, O], when the aldehyde is (a) liquid, (b) gaseous.

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i.e. [C'H'O, O']=2 [C, O2]+2 [H2, O]-[C2, H', O]= 275,500
but 2 [C, O2]+2 [H2, O]

(b) Gaseous: data,

=330,600

.. [C2, H, O] liquid1= 55,100+.

[C2H4O, O']=266,000; and 2 [H2, O]=117,400 :
(gaseous)

(gaseous)

.. [C2, H1, O] gaseous=45,200.

K. If the products of a reaction are gaseous and are maintained at a high temperature, it becomes necessary to introduce corrections for the specific heats, and heats of vaporisation, of these products, into the calculation of the thermal value of the reaction.

Thus, required the thermal value of the reaction [C'H3, O'] at 150°.

Data,

C2H2+O5=2CO2+ H2O, [or C2H2, O3]
(liquid)

at ordinary temperatures (20°)=2 [C, O2]+[H2, O]-[C2, H2]=310,600 :
but thermal capacity of 2 gram-molecules of CO, for tem-
perature-interval 20°-150°

...

=

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2482 units. (a) 1 mol. liquid H2O 20°—100° = 18.80= 1440 thermal capacity of (6) heat of vaporisation of do. at 100° I gram-molecule of H2O

= 18.536'5

(c) thermal capacity of 1 mol. steam
100°-150° = 18.50.0*4805

=

9657"

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total=14011 units.

1 The CO2 produced is gaseous; the heat of formation of liquid CO, is unknown.

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