For a given solution if density is 1 g/ml then say whether molality is greater then molarity or not?
Answers
Answer:
Explanation:
If you want to get picky about it, this is only necessarily true when the solvent is water. The density of water is about 1 kilogram per liter, and that fact is at the heart of the explanation you seek.
When you calculate molarity, you divide moles of solute by liters of solution. You can dilute any solution to one liter, regardless of how many moles of solute it contains, and have a denominator of 1 L.
Molarity=moles of soluteliters of solution
When you calculate molality, however, you divide moles of solute by kilograms of solvent.
molality=moles of solutekilograms of solvent
Adding solute to water necessarily means that the mass of water must decrease for a given volume. In other words, if you compare one liter of water to one liter of, say, a sulfuric acid solution, the sulfuric acid solution contains a lower mass of water. Ergo, when you’re calculating the molality of said solution, you’re dividing by a lower number, which gives you a higher result.
Suppose, for example, that you have a 20%w/w solution of H2SO4, the density of which (at 20ºC) is 1.18 g/cm³. One liter (1000 cm³) of the solution therefore has a mass of 1180 grams, 20% of which (236 grams, or 2.41 moles) is made of sulfuric acid, and the rest (944 grams, or 0.944 kilograms) is water.
The molarity of said solution is:
Molarity=2.41 mol1 L=2.41 M
And the molality is:
molality=2.41 mol0.944 kg=2.55 m
Which seems to prove your case. But what if the solvent isn’t water?
Carbon tetrachloride is a nonpolar solvent whose density is about 1.59 times greater than water, so about 1.59 kilograms per liter. Unlike water, there aren’t many data tables available online that give the densities of various CCl4 solutions; ergo, we’ll refer to a very dilute solution of, say, iodine, I2, so that the density is reasonably close to the density of pure CCl4.
Suppose you prepare a 0.5%w/w solution of iodine in CCl4. Because the solution is so dilute, we’ll assume that its density is approximately the same as the density of the pure solvent: 1.59 kg/L. So one liter of the solution would have a mass of 1590 grams, 0.5% of which (7.95 grams or 0.0313 mol) is iodine, and the remainder (about 1580 grams or 1.58 kilograms) is CCl4.
The molarity of this solution is:
Molarity=0.0313 mol1 L=0.0313 M
And the molality is:
molality=0.0313 mol1.58 kg=0.0198 m
When the solvent is significantly more dense than water, the molality winds up being less than the molarity.
So…your premise is true if the solvent in question is water, or a solvent less dense than water.
The molality will be greater than the molarity.
Explanation:
The molality will be greater than the molarity.
- Molarity = number of moles of solute/ liter of solution
- Molality = number of moles of solute/ kg of solvent
The numerator ( number of moles of solute) is the same in both cases.
We need to find the difference in the denominator term.
In case the density of solvent is 1 g/mL, then the volume and mass of the solution would be the same.
But, in the case of the solvent, the mass and volume may not be the same.
The density of solvent will be less, thus mass will also be less.
So, the molality will increase.