How to Calculate the Percentage of Gold in a Mixture

What is the percentage of gold in a mixture with a density of 15.5 g/cm³, containing gold (19.3 g/cm³) and lead (11.4 g/cm³)? The percentage of gold in the mixture, with a density of 15.5 g/cm³, containing gold (19.3 g/cm³) and lead (11.4 g/cm³), is approximately 33.33%. This calculation is based on a weighted average formula considering the densities of gold and lead in the mixture.

Calculating the Percentage of Gold in the Mixture

Given:

Density of gold (D[gold]) = 19.3 g/cm³

Density of lead (D[lead]) = 11.4 g/cm³

Density of the mixture (D[mixture]) = 15.5 g/cm³

Formula:

The formula for calculating the density of a mixture based on its components' densities and percentages is: D[mixture] = (X[%] * D[gold]) + [(100 - X[%]) * D[lead]] / 100

Calculation:

Plug in the values:

15.5 g/cm³ = (X[%] * 19.3 g/cm³) + [(100 - X[%]) * 11.4 g/cm³] / 100

Now, simplify the equation:

15.5 = (X * 19.3) + (100 - X) * 11.4 / 100

Isolate X and solve for X:

X ≈ 0.3333

Convert X to a percentage:

X[%] ≈ 33.33%

Therefore, the percentage of gold in the mixture is approximately 33.33%.

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