250 ml of seawater and we inked each molecule with pink color, then we mixed this 250 ml in the ocean. After mixing you took 250 ml of seawater. How many pink molecules in the 250 ml after mixing the ocean?

9.77 × 10⁹ molecules

Explanation:

Since the density of water is 1 g/cm³ = 1000 g/L

So, we find the mass of sea water in 250 mL = 0.250 L

We know density = mass/volume

mass = density × volume = 1000 g/L × 0.250 L = 250 g

Now we calculate the number of moles of sea water in 250 g, 250 mL of sea water.

number of moles n = mass of sea water,m/molar mass of water, M

molar mass of water, M = 18 g/moL

n = m/M = 250 g/18 g/mol = 13.89 mol

We now calculate the number of molecules present in the 250 mL of sea water.

n = N/N' where N = number of molecules, N' = avogadro's number = 6.022 × 10²³/mol

So,N =nN' = 13.89 mol × 6.022 × 10²³/mol = 8.36 × 10²⁴ molecules

Now, the volume of the ocean is 1.337 × 10¹⁸ m³ = 1.337 × 10¹⁵ L

Since the 250 mL sea water is mixed with the ocean, the number of molecules per liter is 8.36 × 10²⁴ molecules/1.337 × 10¹⁵ L = 6.25 × 10⁹ molecules/L

If we now take 250 mL out of the ocean, the number of molecules in this 250 mL will be 6.25 × 10⁹ molecules/L × 250 mL =  6.25 × 10⁹ molecules/L × 0.250 L = 9.77 × 10⁹ molecules.

So, we have 9.77 × 10⁹ molecules of pink molecules in the 250 mL after mixing in the ocean.