Alvin Cheung Student# 1001204074 TA: Rabia Saleem

CHM110H5F Assignment 1

!For the aqueous solutions at 25C whose concentrations were considered in the lectures, an

interesting observation was made. In each case, the concentration when expressed in units of

molality was numerically greater than the concentration when expressed in units of molarity.

Do you think that this is a general rule for aqueous solutions? Explain your reasons. Are there

solutions for which you think the molality might be less than the molarity? Explain.

The general expression for molarity and molality can be demonstrated in the equations

above. The premise of concentration expressed in units of molality is numerically greater than the

concentration expressed in units of molarity is indeed a general rule for aqueous solutions. The

concentration expressed in units of molality is in terms of the mass of solvent, whereas the

concentration expressed in units of molarity is in terms of the volume solution, which accounts for

the volume of solute and solvent, which causes the denominator of the molaritys calculation to be

greater than the denominator of the molalitys calculation. Hence, the overall value of molality is

generally greater than molality. For instance, in reference to figure 1, the model for molarity

illustrates that there contains 1 mole of HCl in 1 liter of HCl solution (HCl + H2O). On the other

hand, the model for molality illustrates that there contains 1 mole of HCl in 1Kg of H2O. Since the

denominator of the calculation of molarity is always greater than the denominator of molarity,

the value for molality will always be greater than molarity.

!!!!!

M =Molarity = n(solute)L(solution)

m =Molality = n(solute)Kg(solvent)

MolalityMolarity

1 mole of HCl

1Kg of H2O

1 mole of HCl

1L of HCl Solution

Figure 1

Alvin Cheung Student# 1001204074 TA: Rabia Saleem!

There are possible solutions for which the molality value is less than the molarity value,

where the density of solvent is greater than 1gmL-1. Solvent such as HCl tend to have a higher

density than 1gmL-1, hence could be used as an example for this situation. For example, given that

calcium carbonate (CaCO3) is being dissolved in 1 liter of hydrochloric acid (HCl), with the density

of 1.49gmL-1, the value of molality is less than molarity.

!!!!!!!!!!!!!!! For the example above, it shows that when the density of the solute is greater than 1gmL-1,

the value of molality will be less than molarity. Therefore, the general rule of aqueous solution

where molality is always greater than molarity does not apply when the density of the solute is

greater than 1gmL-1.

density = massvolume

mass = density volume=1.49gmL1 1000mL=1490g=1.490Kg

Molality = n(solute)Kg(solvent)

=1mol(CaCO3)1.490Kg

= 0.671molKg1

Molarity = n(solute)L(solution)

=1mol(CaCO3)

1L=1molL1