The density of methanol at 298k is 0.8. What is the molarity of pure methanol at 298k

A. 1. B.0.8. C. 55.5. D. 29.8. E. 73.4

To determine the molarity of pure methanol at 298 K, we need to understand the relationship between density, molarity, and the molecular weight of methanol. Molarity is defined as the number of moles of solute per liter of solution. In this case, since we are dealing with pure methanol, we can treat it as the solute and solvent simultaneously.

Understanding Density and Molarity

The density of methanol is given as 0.8 g/mL. This means that 1 mL of methanol weighs 0.8 grams. To find the molarity, we first need to convert this density into a more useful form.

Step 1: Convert Density to Grams per Liter

Since molarity is expressed in moles per liter, we need to convert the density from grams per milliliter to grams per liter:

• 1 mL of methanol = 0.8 g
• 1 L = 1000 mL
• Therefore, 1 L of methanol = 0.8 g/mL × 1000 mL = 800 g

Step 2: Calculate Moles of Methanol

Next, we need to find out how many moles are in 800 grams of methanol. The molecular weight of methanol (CH₃OH) is approximately 32.04 g/mol. We can use this to convert grams to moles:

• Moles of methanol = mass (g) / molecular weight (g/mol)
• Moles of methanol = 800 g / 32.04 g/mol ≈ 24.98 moles

Step 3: Calculate Molarity

Now that we have the number of moles, we can calculate the molarity:

• Molarity (M) = moles of solute / liters of solution
• Molarity = 24.98 moles / 1 L = 24.98 M

Final Calculation and Answer

Since we rounded to two decimal places, the molarity of pure methanol at 298 K is approximately 25 M. However, looking at the options provided:

• A. 1
• B. 0.8
• C. 55.5
• D. 29.8
• E. 73.4

The closest answer to our calculated value of 25 M is D. 29.8. Therefore, the correct choice is D. 29.8.