Four parameters are necessary to completely describe a gas: Pressure (P) exerted by the gas, Temperature (T) of the gas, Volume (V) of the container, and the number of moles (n) of gas. Temperature must be reported using the absolute temperature scale, Kelvin. The conversion from Celsius degrees to Kelvin temperature is:

TK = TC + 273.15

(1)

 

According to Boyle's Law, pressure and volume are inversely proportional. The product PV is equal to a constant when temperature and number of moles of gas are held constant. A useful form of Boyle's Law is expressed as:

P1V1 = P2V2

(at constant n and T)

(2)

The everyday knowledge that substances expand when heated, approaches an expression for Charles' Law. The relationship between the volume of a gas and its absolute temperature at constant pressure and number of moles of gas (Charles' Law) is given as:

V1T1 = V2T2

(at constant n and P)

(3)

The Italian scientist Amadeo Avogadro proposed that equal volumes of different gases at the same temperature and pressure contain equal numbers of moles (Avogadro's Law). Combination of Avogadro's law and the laws of Boyle and Charles leads to the ideal gas law

PV = nRT

(4)

where R is the ideal (or universal) gas constant. The value for R depends upon the units of P and V. For pressure in atm and volume in L,

R = 0.08206	L atm
	K mol

In this experiment we will determine the molar volume (Vm) of hydrogen gas at standard temperature and pressure, STP. The molar volume of a gas is the volume that one mole of a gas occupies and has a theoretical value of 22.414 L/mol at STP. According to Avogadro's law, this is the volume of one mole of any gas under standard temperature and pressure conditions. In actuality there are slight differences in the pressure-volume-temperature relationships of real gases. However, gases composed of small, non-polar molecules approach ideal gas behavior.

Hydrogen gas will be generated in this experiment by the reaction of Zn metal with the strong acid HCl(aq). The reaction is described by the unbalanced molecular equation 5.

Zn(s) + HCl(aq) ---> H2(g) + ZnCl2(aq)

(unbalanced)

(5)

If the sample mass of Zn metal is known, the number of moles of hydrogen gas generated can be calculated using the balanced net ionic equation for Equation 5.

The hydrogen gas will be collected over water. To determine the pressure of hydrogen gas (PH2) collected, one must correct for the vapor pressure of water (PH2O). According to Dalton's law, "the total pressure of a gaseous mixture is equal to the sum of the partial pressures of the components". Thus, the pressure of H2 may be determined from Equation 6,

PT = PH2 + PH2O

(6)

where PT is the total pressure of the mixture or, in our case, atmospheric pressure and PH2O is the vapor pressure of water at room temperature, determined from Appendix B.

One can calculate the volume of dry hydrogen (V2) that would have been collected at STP (273.15 K, 760 torr) using Equation 7, an expression of the combined gas laws.

 

P1 and V1 represent the partial pressure and volume, respectively, of H2 collected at the laboratory temperature, T1. Using 273.15 K for T2 and 760 torr (i.e. standard conditions) for P2, V2 can be determined.

The molar volume of hydrogen, Vm in units of L/mol , may then be obtained using Equation 8 where n represents the number of moles of H2 generated and V is its volume (L) at STP.

Vm = V n

(8)