# Ideal Gas Law with Examples

**Ideal Gas Law**

In ideal gas; molecules have no volume and there are no interaction between them. In real there is no such a gas, it is just an assumption. All real gases has small volumes and there are interactions between them. In problem solutions; we assume all gases as ideal gas. Given equation below is ideal gas law. We get it by combining all gas laws given in last section.

**P.V=n.R.T**

Where; **P** pressure, **V** volume, **n** number of particles, **R** gas constant 0,08206 L atm / K mol or 22,4/273 L atm / K mol, and T temperature

Now we solve some problems related to ideal gas law for better understanding, follow each example carefully.

**Example:** Find pressure of 8,8 g CO_{2} at 27 ^{0}C in container having volume 1230 cm^{3}. (C=12, O=16)

**Solution:** We first find molar mass of CO_{2};

CO_{2}=12+2.16=44

Then, we find moles of CO_{2};

n=8,8/44=0,2 moles

Converting temperature from ^{0}C to K and volume from cm^{3} to liter;

T=27+273=300 K

V=1230 cm^{3}=1,23 liters

Now, we use ideal gas law to find unknown quantity.

P.V=n.R.T

P.1,23=0,2.0,08206.300

P=4 atm

**Example:** Find molar mass of X(gas) given in the picture below having volume 896 cm^{3}, temperature 273 ^{0}C and mass 0,96g. (O=16, and atmospheric pressure is 1 atm )

**Solution:**

We make unit conversions first.

P=38 cm Hg=38/76=0,5 atm

V=896/1000=0,896 liters

T=273 + 273=546 K

Now, we use ideal gas law to find n;

P.V=n.R.T

0,5.0,896=n.(22,4/273).546

n=0,03 moles

Molar mass of X;

M_{X}=m_{X}/n=0,96/0,03

M_{X}=32 g/mol

Thus; X(gas)=O_{2}

**Example:** System given below is placed in a location having 70 cm Hg atmospheric pressure. Container has 2 g He at first, then we add 1 g H_{2} gas to this container. Find the rising of Hg in the manometer after adding H_{2}. (He=4, H_{2}=2)

P_{initial}=P_{0}-20=70-20=50 cm Hg

n_{initial}=2/4=0,5mol He

n_{H2}=1/2=0,_{}5mol H_{2}

n_{final}=n_{He}+n_{H2}

n_{final}=0,5+0,5=1mol

We write ideal gas law for initial and final values, then we dive them each other to find unknown value.

V and T are constant in two situations.

P_{final}=100 cm Hg

Difference between levels of Hg between two branches of manometer;

100-70=30 cm in right branch of manometer

Thus difference between initial and final levels of Hg becomes;

20+30=50 cm

This change is shared by two branches of manometer ;

50/2=25 cm

Thus, Hg rises 25 cm in one branch of manometer.