chemistry moles of solute

Question

Calculate the number of moles of solute in 85.25 mL of 0.1655 M K₂Cr₂O7(aq).

please explain how to do this easily this is my worst subject and no matter how much i study it doesnt seem to help. Not a fan of online learning.

Answer 1

Hi Taylor!

The most important concept to understand when approaching this problem is the relationship between 3 values of a given solution: Concentration, Volume, and the # Moles of Solute Dissolved.

As a basic definition, Concentration describes how much solute dissolves in a given volume of solution. Thus, a general equation for concentration can be written:

Concentration = Amount of Solute / Volume

This equation gives a very general definition of Concentration. Often in chemistry, however, we want to specify standard units. Most commonly, we define the amount of solute to be in terms of # of Moles, and the volume to be in terms of Liters.

When using these specific units, the equation for Concentration can be rewritten as:

Concentration = # Moles of Solute / Liters of Solution

This Concentration is called the Molar Concentration (or Molarity) and is given in the units [ # Moles of Solute/ Liter]. Basically, Molarity describes how many moles of a given solute can be dissolved in 1 Liter of solution.

Just so we don't get confused, we will rewrite the above equation but now call Concentration Molar Concentration:

Molar Concentration = # Moles of Solute / Liters of Solution

We can rearrange this equation to solve for # Moles of Solute by multiplying both sides by Liters of Solution

# Moles of Solute = Molar Concentration * Liters of Solution

This equation can be used for any solution.

Now that we understand this relationship, we can plug in our given values! We know that our solution has a Molar Concentration of 0.1655 Moles/Liter (M stands for Moles/Liter and tips us off to the fact that this is indeed a Molar Concentration). We also know that our volume is 85.25ml. Unfortunately, in order to plug volume into our equation for # Moles Solute, our volume must be in Liters. Luckily, we can use unit conversion to easily find our volume in L. Below I have outlined 2 approaches to doing this:

Dimensional Analysis Approach:

We know that:

1 L = 1000mL

If we divide both sides by 1000mL, we get

1 = 1L/1000mL

This expression is called a conversion factor. It is equal to one and contains a numerator and denominator with different units. We will use this conversion factor to convert our Volume for mL to L. To do so, we first write out

Volume = 85.25mL

We then multiply this volume by our conversion factor

Volume = 85.25mL * (1L / 1000mL)

We are allowed to do this because 1L/1000mL is equal to 1, and thus we are really just multiplying our volume by 1, which doesn't change its value. However, it does change the units! Because there are now units of mL in both the numerator and denominator, this unit cancels out and we are left with

Volume = 85.25 L / 1000

or

Volume = 0.08525 L

What we just did is called dimensional analysis and is super useful in chemistry. Often times for more complicated problems, we will multiply by multiply different conversion factors, cancelling out units until we are left with the units that we want.

Reasoning Method

The dimensional analysis method of unit conversion may seem tricky at first, but is a very useful skill. If you are struggling to understand it, however, you can also reason your way through the conversion. We know that 1 mL is 1000x smaller than 1 L. Thus, it makes sense that a volume will appear 1000x larger when represented in these smaller units than if it were to be represented in Liters. The volume in Liters would look 1000x smaller. Thus, to get from mL to Liters, we have to divide by a factor of 1000.

Regardless of what method you choose, you will come across the same answer:

Volume = 0.08525L

Now all we have to do is plug in our Volume and Molar Concentration into the equation:

# Moles of Solute = Molar Concentration * Liters of Solution

#Moles of Solute = 0.1655M K₂Cr₂O₇ * 0.08525L

Remember that M stands for Moles/Liter, so:

# Moles of Solute = (0.1655 moles K₂Cr₂O₇ / L) * 0.08525L

Liters cancel out and we are left with:

# Moles of Solute = 0.0141 Moles K₂Cr₂O₇

Hope that this explanation helped!