Molarity of Water- Molarity, Molarity of Pure Water, Practice Problems, Frequently Asked Questions

Hey, could you please answer one of my very simple molarity questions? My question is, "What should be the molarity of 18 g of pure water at 298 K?"

But, molarity is calculated for a solution and not for pure substances…? I know that, everyone is intrigued that the information is incomplete. right?????

You can easily calculate the molarity of this solution by reading the provided information for any weight or volume of pure water at 298K. Let's learn something new about molarity.

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Table of Contents

Molarity
Molarity of pure water
Practice Problems
Frequently Asked Questions

Molarity

The amount of a substance in a specific volume of solution is known as its molarity (M). The number of moles of a solute per litre of a solution is known as molarity. The molar concentration of a solution is another name for molarity.

$M o l a r i t y = \frac{N u m b e r o f m o l e s}{V o l u m e o f s o l u t i o n s (L)}$

If the volume is given in mL

$M o l a r i t y = \frac{N u m b e r o f m o l e s}{V o l u m e o f s o l u t i o n s (m L)} \times 1000$

Molarity of pure water

The molarity of pure water [H2O]can be calculated as follows:

$M o l a r i t y o f p u r e w a t e r = \frac{N u m b e r o f m o l e s}{V o l u m e o f s o l u t i o n s (L)}$

Density of pure water $= \frac{M a s s}{V o l u m e} = 1 g c m^{- 3} o r 1000 k g m^{- 3}$

Hence, if the volume of pure water = 1 L or (1000 mL or cm3)

$\frac{M a s s o f p u r e w a t e r}{1000 {c m}^{3}} = 1 {g / c m}^{3}$

Mass of pure water = 1000g

Moles of pure water = $\frac{1000}{18} = 55.55$ moles

Molarity of pure water $= \frac{N u m b e r o f m o l e s}{V o l u m e o f s o l u t i o n s (L)} = \frac{55.55 m o l e s}{1 L} = 55.55 m o l L^{- 1} = 55.55 M$

So, this is clear that for any weight or volume of pure water at 298 K, the value of molar concentration is fixed and equals to 55.55 M.

Practice Problems

1. Assertion: The molarity of pure water is calculated as 55.55M at 298K.

Reason: Molarity depends upon temperature.

a. Both assertion and reason are correct and Reason is the correct explanation for Assertion.
b. Both assertion and reason are correct but the reason is not the correct explanation for assertion.
c. Assertion is correct but reason is incorrect.
d. Assertion is incorrect but reason is correct.

Solution: It is true that molarity of pure water is calculated as 55.55 M at 298 K and it is also true that molarity depends upon temperature. But the second statement is not a correct explanation of the prior one because temperature dependence is one of the properties of molarity but the fixed value of molarity at 298 K is due to the density of pure water. Hence the correct answer is an option (B).

2. What should be the value of molarity of 500 g pure water at 298K?

a. Data insufficient
b. 55.55 M
c. 5.55 M
d. 50 M

Solution: Mass of pure water = 500 g

Density of pure water $= \frac{M a s s}{V o l u m e} = 1 g c m^{- 3} o r 1000 k g m^{- 3}$

$\frac{500 g}{V o l u m e o f p u r e w a t e r} = 1 {g / c m}^{3}$

Volume of pure water $= \frac{500}{18} = 27.77 m o l e s$

Moles of pure water = 50018=27.77 moles

$M o l a r i t y o f p u r e w a t e r = \frac{N u m b e r o f m o l e s}{V o l u m e o f s o l u t i o n s (m L)} \times 1000 = \frac{27.77 m o l e s}{500 m L} \times 1000$

Molarity of pure water = 55.55 molL-1= 55.55 M

Hence, the correct answer is an option (B).

3. Calculate the weight of water with 55.55 M molarity and at 298K?

(Density of pure water = 1gcm-3or 1000 kgm-3)

Solution: Let us suppose the mass of pure water = x g

Density of pure water = Mass Volume = 1gcm-3or 1000 kgm-3

$\frac{x g}{V o l u m e o f p u r e w a t e r} = 1 {g / c m}^{3}$

Volume of pure water = x cm3 or x mL

Moles of pure water = x18 moles

$M o l a r i t y o f p u r e w a t e r = \frac{N u m b e r o f m o l e s}{V o l u m e o f s o l u t i o n s (m L)} \times 1000 = \frac{\frac{x}{18} m o l e s}{x m L} \times 1000 = \frac{1000}{18}$

Molarity of pure water = 55.55 molL-1= 55.55 M

In the calculation we considered x gram (= x mL) of water.

Since the density of water is one, solution volume= solution weight, so that molarity formula contains neither volume nor the weight of water, making molarity a constant for any volume or weight of water.

Molarity of water is independent of weight or volume of water .So any weight is acceptable for this molarity.

4. Calculate the molarity of the solution in which 100 g of platinum powder is added to 700 g of pure water at 298 K. (MM of Platinum = 195 g)

a. 55.55 M
b. Data Insufficient
c. Molarity is not defined for such kinds of mixtures
d. 0.732 M

Solution: Platinum powder is insoluble in water and hence can not make a solution. Molarity is specifically defined for solutions, not for mixtures. Therefore we are not able to calculate the molarity in this case.

Hence, the correct option is (C).

Frequently Asked Questions

1. What distinguishes molality (M) from molarity (m) fundamentally?
Answer: In contrast to molality, which is defined as the number of moles of solute found in 1 kilogramme of solvent, molarity is the concentration of a material that is computed as the number of moles of solute that are dissolved in 1 litre of solution. The second major difference is that there is no volume term present in molality which makes it temperature-independent whereas molarity is temperature-dependent as contains a volume term in the denominator.

2. Which of the following molality or molarity depends on pressure?
Answer: Only the mass of the solvent affects molarity; however, the volume of the solution also affects molarity, and both pressure and temperature can affect volume. Further, unlike molality, molarity is influenced by pressure.

3. Which is preferable if we are working with a variety of temperatures: molality or molarity?
Answer: We are aware that molality is independent of temperature. Therefore, while working with a range of temperatures, molality will be easier to apply.

4. 1M or 1m: Which has a higher concentration?
Answer: One molar solution, or 1M, contains 1 mole of solute in a 1litre solution, which includes both the solute and the solvent. On the other side, 1m stands for 1 molal solution, which is made up of 1 mole of solute in 1 kg, or roughly 1 litre, of solvent. Now that we can clearly see it, 1M and 1m solutions both contain one mole of solute, but the 1 M solution contains a larger amount of solvent. As a result, 1M has a higher concentration than 1m.

5. Which is advisable when working with a temperature range: molality or molarity?
Answer: We already know that molality does not change with temperature. As a result, when working with a wide range of temperatures, molality will be more convenient to use.