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Application of Gay-Lussac’s Law of Combining Volumes

Gay Lussac’s of combining volumes states that gases react in simple ratio with one another and to volumes of the products provided that temperature and pressure remain constant. In this article, you will understand how to apply this law in calculation by studying the following examples below: 1.     2H 2 + O 2 → H 2 O In the reaction above, what volume of hydrogen would be left over when 300cm 3 of oxygen and hydrogen are exploded in a sealed tube?   1cm 3 of oxygen = 2cm 3 of hydrogen 300cm 3 of oxygen = 2 x 300 = 600cm 3 Volume of left over = 1000 – 600 = 400cm 3 2.     Calculate the volume of carbon (II) oxide required to react with 40cm 3 of oxygen. 2CO + O 2 → 2CO 2 1cm 3 of oxygen = 2cm 3 of CO 40cm 3 of oxygen = 2 x 40 = 80cm 3 3.     Calculate the volume of residual gases that would be produced when 100cm 3 of sulphur (IV) oxide reacts with 20cm 3 of oxygen    2SO 2 + O 2 → 2SO 3 1cm 3 of O 2 = 2cm 3 20cm 3 of O 2 = 2 x 20 = 40cm 3
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How to calculate velocity of sound wave at a given temperature


 Question 1

A source of sound wave of frequency 660Hz emits waves of wavelength 0.12m in air at 40oC. What is the velocity of sound wave in air at this temperature? What would be the wavelength of sound wave from the source in air at 70oC?

 

Answer

Frequency = f = 660Hz

Wavelength= λ = 0.12m

Temperature = 40+273 = 313K

Velocity of sound wave at 400C

V = fλ = 660 x0.12 =79.2m/s

Wavelength of wave at 700C

Note: to find the wavelength, we must find the velocity of the sound wave at 700C. Velocity of sound wave is directly proportional to the square root of its temperature in kelvin.

V1/V2 = √T1/√T2

V1 = 79.2m/s

T1 = 313K

T2 = 70 + 273 = 343K

79.2/V2 = √313/√343

79.22/(V2)2 = 313/343

313(V2)2 = 79.22 x 343= 2151515.52

(V2)2 = 2151515.52/313

(V2)2 = 6873.9

V2  = √6873.9   = 82.9m/s

Since V=fλ then

82.9 = 660 x λ

.λ = 82.9/660 =0.13m

 

Question II

A sound wave of velocity 200m/s, calculate the temperature of the wave, if the velocity of sound wave in air is 330m/s at 00C.

Answer

Velocity = V2 = 200m/s

Temperature = T2 =??

Velocity = V1 = 330m/s

Temperature = T1 = 273+0 = 273K

V1/V2 = √T1/√T2

330/200 = √273/ √T2

3302/2002 = 273/T2

T2 = 2002x273/ 3302    = 10920000/108900

         = 100.3K or -1730C

Question III

The velocity of sound wave in air is 330m/s at 00C. What would be its velocity if the temperature is increased to 1000C? What is the change in velocity of the wave?

 

Answer

V1 = 330m/s

T1 = 0+273 =273K

V2 =??

T2 = 100+273 =373K

Velocity of wave at 1000C

V1/V2 = √T1 /√T2

330/V2 = √273/ √373

3302/(V2)2 = 273/373

(V2)2 = 330x330x373/273

      = 148790.1

V2 = √148790.1 = 385.7m/s

Change in velocity

V2  - V1 = change in velocity

385.7-330 = 55.7m/s

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Application of Gay-Lussac’s Law of Combining Volumes

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