Q. The relationship between molarity (M) and molality (m) for a solution with density d (g/mL) and molar mass of solute M is:

घनत्व d (g/mL) और विलेय M के दाढ़ द्रव्यमान वाले घोल के लिए मोलरता (M) और मोलरता (m) के बीच संबंध है:

M = m × d
एम = एम × डी

M = m / (1 + 0.001 × m × M)
एम = एम / (1 + 0.001 × एम × एम)

M = m × d / (1 + 0.001 × m × M)
एम = एम × डी / (1 + 0.001 × एम × एम)

M = m / d
एम = एम / डी

To derive the relationship:

Let's consider 1 kg of solvent containing m moles of solute:

Mass of solute = m × M (where M is molar mass)

Total solution mass = 1000 g + (m × M) g

Solution volume = Total mass ÷ density = [1000 + (m × M)] ÷ d

Molarity = moles of solute ÷ volume of solution (in L)

M = m ÷ {[1000 + (m × M)] ÷ d} × (1/1000)

M = m × d ÷ [1000 + (m × M)] × 1000

M = m × d ÷ [1 + 0.001 × m × M]

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