How to Calculate the Percentage of Gold in a 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%.