Answer:
To prove that the mass concentration (ρ) is equal to the product of the mole concentration (C) and the molar mass (M), we can use basic principles of chemistry and mathematics.
The mass concentration (ρ) is defined as the mass of the solute (m) divided by the volume of the solution (V):
ρ = m / V
The mole concentration (C) is defined as the number of moles of solute (n) divided by the volume of the solution (V):
C = n / V
The molar mass (M) of a substance is defined as the mass of one mole of that substance. Therefore, the mass of the solute (m) can be expressed as:
m = n * M
Now, we can substitute this expression for m into the mass concentration equation:
ρ = m / V
ρ = (n * M) / V
Since C = n / V, we can express n as:
n = C * V
Now, substitute this expression for n into the equation:
ρ = (C * V * M) / V
Now, we can see that the volume (V) cancels out, leaving us with:
ρ = C * M
So, we have successfully shown that the mass concentration (ρ) is equal to the product of the mole concentration (C) and the molar mass (M):
ρ = C * M
This equation is a fundamental relationship in chemistry and is used to relate the mass concentration, mole concentration, and molar mass of a substance in a solution.
Step-by-step explanation: