Hello, I am back with the gas equations the first equation I will be talking about is
General Gas Equations
From the gas laws,we know that the volumes of a gas depends on it's temperature and pressure.
The relationship between the variables are summed up as follows;
If V=K÷P
And V=KT
Then V=KT÷P
Making K the subject of the formula
K= VT÷P
But Boyle's law is PV=K
& Charles' Law is V÷T=K
Thus PV÷T=K
If for a fixed mass of gas V1 is the volume at temperature T1 & pressure P1 and V2 is the volume at temperature T2 & pressure P2.
Then General gas equation is given as
P1V1÷T1=P2V2=T2
Before solving problems as examples, I would like to tell you that pressure and temperature has it's standard form. It is the Standard Temperature and Pressure (STP).
Temperature has it's standard form as 273 Kelvin.
Pressure has it's standard form as 760mmHg or 1.01×10⁵Nm-².
Let's solve a problem involving STP and general gas equation
At STP, a certain mass of gas contain 790cm³. Find the temperature at which the gas occupies 1000cm³ and pressure 726mmHg
Solution
P1V1÷T1=P2V2÷T2
P1=760mmHg
V1=790cm³
T1=273k
P2=726mmHg
V2=1000cm³
T2=?
P1 V1÷T1=P2V2÷T2
Cross multiply
P2V2 T1÷P1V1T2
Make T2 subject formula
T2=P2V2T1÷P1V1
T2=726×1000×273÷760×790
T2=330.1k
Ideal Gas Equations
Four quantities are important in all experimental work, measurement or calculation involving gas
- Volume
- Pressure
- Temperature
- Number of moles.
Where
V=volume
P=pressure
T=temperature
R=number of moles
Thus, Ideal gas equation is;
PV=RT
Where;
R is a constant termed as the molar gas constant. The Ideal gas equation holds true for all gases. The above equation applies only to one mole of gas. For n moles of gas we get the general form of equation
PV=nRT
Where;
P is in atmosphere (atm)
V in decimeters cube (dm³)
T in Kelvin
n=number of moles of gas.
At STP, for one mole of gas R=PV÷nT
R=(1atm)(22.4dm³)÷(1mol)(273k)
R=0.082atmdm³k-¹mol-¹
Let's solve a problem as example
A certain amount of gas occupies 5.0dm³ at 2atm and 10°c. Calculate the number of moles present (R=0.082atmdm³k-¹mol-¹)
Solution
n=PV÷RT
P=2atm
V=5.0dm²
T=10+273=283k
R=0.082atmdm²k-¹mol-¹
.•. n=2×5.0÷0.082×283
n=0.431mol.
With that I have to the end of Gas Laws and calculation. Thanks for stopping by ❤️❤️❤️