Question

The molarity of pure water at \(277 \mathrm{~K}\) is (a) \(1 \mathrm{M}\) (b) \(5 \mathrm{M}\) (c) \(55.5 \mathrm{M}\) (d) \(2.5 \mathrm{M}\)

Short answer

The molarity of pure water at 277 K is 55.5 M (option c).

Step-by-step solution

Understanding Molarity

Molarity is a measure of the concentration of a solution, expressed as the number of moles of solute per liter of solution. For pure substances like water, we calculate the molarity based on water's density and molar mass.

Calculating Water's Density

At 277 K (or 4°C), water has its maximum density, around 1 g/cm³, which is equivalent to 1000 g/L.

Converting to Moles

To find the number of moles of water in 1 liter, divide the density by the molar mass of water. The molar mass of water (H₂O) is approximately 18.015 g/mol. Calculate the moles: \[ \text{Moles of water} = \frac{1000 \text{ g/L}}{18.015 \text{ g/mol}} \approx 55.5 \text{ moles/L} \]

Identifying the Molarity

Now that we have calculated the number of moles of water in 1 liter, this value directly represents the molarity of pure water. Hence, the molarity of pure water at 277 K is 55.5 M.

Key concepts

Understanding the Density of Water

Water is a fascinating substance, not just because it is essential for life, but also due to its unique physical properties. One key property is its density, which is highest at 4°C (or 277 K). At this temperature, water has a density of about 1 gram per cubic centimeter (g/cm³). This means that in 1 liter, which is equivalent to 1000 cubic centimeters, you have 1000 grams of water.
Understanding the density of water is fundamental because it allows you to convert between the mass of water and its volume easily. This conversion is particularly useful in calculations involving molarity, where knowing how much water you have in terms of volume and mass is necessary.
Keep in mind:

• The density surprisingly decreases as water freezes or gets even hotter, but at 277 K, it peaks.
• This maximum density trait is why lakes freeze from the top down, insulating aquatic life below.

Importance of Molar Mass in Calculations

Molar mass is basically a measure of how much one mole of a substance weighs. For water, with its chemical formula H₂O, the molar mass is about 18.015 grams per mole. You calculate this by adding up the atomic masses of all the atoms in a molecule of water.
To break it down:

• Hydrogen (H) has an atomic mass of approximately 1.008 g/mol and there's two hydrogens, so that adds up to about 2.016 g/mol.
• Oxygen (O) has an atomic mass of about 16.00 g/mol.

Add these up to get water's molar mass. This calculation is essential for converting the mass of a substance into moles, a step needed in determining concentration like molarity.
This foundational step ensures accuracy when analyzing how concentrated so-called solutions are, even in the case of a paradoxically pure substance like water itself.

Measuring Concentration Through Molarity

Molarity is a crucial concept in chemistry when it comes to understanding the concentration of solutions. It is expressed in moles per liter (M). In simpler terms, molarity tells you how much solute, or substance, there is in a solution compared to how much total solution you have.
When calculating the molarity of pure water, you're essentially measuring how many water molecules you can fit in a liter. Here's how you do it:

• First, use water's density to find out the mass in a certain volume.
• Then, divide that mass by water's molar mass to find out how many moles are in that volume.

In the specific case at 277 K, we calculated that there are about 55.5 moles of water per liter. So, the molarity of pure water is 55.5 M.
Understanding molarity provides valuable insights into solution properties, allowing for rigorous scientific explorations like determining the effects of temperature on water at a molecular level.