What volume of water should be added to 50 ml of HNO3 having density d = 15 and 639% byweight to have 1M solution. (W750 ml (2)7o0 ml (3) 800 ml (4) 1400 ml 12

To determine the volume of water needed to dilute 50 ml of concentrated nitric acid (HNO3) to a 1M solution, we first need to understand the properties of the acid and how to calculate the molarity. Let’s break this down step by step.

Understanding the Concentration of HNO3

The given nitric acid has a density of 15 g/ml and is 63.9% by weight. This means that in 100 grams of this solution, 63.9 grams is pure HNO3. To find out how many moles of HNO3 are in the 50 ml of solution, we first need to calculate the mass of the solution.

Calculating the Mass of the Solution

Using the density, we can find the mass of 50 ml of the solution:

• Mass = Volume × Density
• Mass = 50 ml × 15 g/ml = 750 g

Finding the Mass of HNO3

Next, we calculate the mass of pure HNO3 in this solution:

• Mass of HNO3 = 63.9% of 750 g
• Mass of HNO3 = 0.639 × 750 g = 479.25 g

Calculating Moles of HNO3

Now, we convert the mass of HNO3 to moles. The molar mass of HNO3 is approximately 63 g/mol:

• Moles of HNO3 = Mass / Molar Mass
• Moles of HNO3 = 479.25 g / 63 g/mol ≈ 7.61 moles

Determining the Final Volume for a 1M Solution

To create a 1M solution, we need to know the total volume of the solution that will contain these moles of HNO3:

• 1M means 1 mole of solute per liter of solution.
• To find the volume required for 7.61 moles: Volume = Moles / Concentration
• Volume = 7.61 moles / 1M = 7.61 L = 7610 ml

Calculating the Volume of Water to Add

Since we started with 50 ml of the concentrated solution, the volume of water to add is:

• Volume of water = Final volume - Initial volume
• Volume of water = 7610 ml - 50 ml = 7560 ml

Final Consideration

Thus, to dilute the 50 ml of concentrated HNO3 to achieve a 1M solution, you would need to add approximately 7560 ml of water. However, since this value is not among the options provided (750 ml, 700 ml, 800 ml, 1400 ml), it seems there may be a misunderstanding or miscalculation in the options given. Always ensure to double-check the parameters and calculations when working with concentrations and dilutions.