Gas Law Notes Chemistry Semester II Ideal Gas Law Combined Gas Law And Guy Lussac’s Law

Ideal Gas Equation  The variables of the physical nature of gases:  n : the number of particles (moles)  P : pressure  V : volume  T : temperature expressed always in K

Ideal Gas Equation  Charles stated that volume varies directly with temperature  Boyle stated volume varies inversely with pressure  So…combining these notions, we can set pressure * volume = to a constant * temperature, where the constant is the same every time it is calculated.  Mathematically this is shown…

Ideal Gas Law Boyle’s Law pressure times volume = a constant Charles’ Law: volume is proportional to temperature Combining the two yields the ideal gas law Restated Ideal Gas Law: …

Ideal Gas Law nR is a constant, n is the moles and R is the universal gas constant R =8.31 L kPa /mol K

Ideal Gas Law Problem  What is the volume of a container holding 2.00 moles of a substance at kPa and 500K?

Problem Set Up  P = kPa  V = ? n = 2.00 moles T = 500K R = 8.31 L kPa/moles K  PV = nRT

Problem cont’d  *V = 2.00*8.31*500  V = 9.99 L

Combined Gas Law  Lab experiments are rarely at STP, usually mathematical corrections must be made.  Corrections are made by multiplying of the original volume (V 1 ) by 2 ratios (1 for temperature and the other for pressure)  The math derivation looks like this:

Combined Gas Law Or… Since n is the same on both sides of the equation…

Combined Gas Law

Combined Gas Law Problems  A 7.51 m kPa and 5 °C should be corrected to STP. What is the new volume?  P 1 V 1 = P 2 V 2 T 1 T 2

Set Up  V 1 = 7.51 m 3  P 1 = 59.9 kPa  T 1 = 5 °C  P 2 = kPa  T 2 = 0 °C  V 2 = ? Find this  Remember convert T to Kelvin!  Now solve it!

Solution  59.9 * 7.51 = * V  59.9 * 7.51 * 273 = V *  V 2 = 4.36 m 3

next question…  Another problem: A helium balloon with volume = 410mL is cooled from 27 °C to -27 °C. P is reduced from 110 kPa to 25 kPa. What is the new V of the lower temp. and pressure?

Set Up  V 1 = 410 mL  P 1 = 110 kPa  T 1 = 27 °C  P 2 = 25 kPa  T 2 = -27 °C  V 2 = ? Find this

Answer  V 2 = 1479 mL

Guy Lussac’s Law Guy Lussac’s Law relates pressure and temperature…. To be used when volume and moles are kept constant