To obtain 500.0 g of nickel, approximately 1147.29 grams of ore are needed.
To find the amount of ore needed to obtain 500.0 g of nickel, we can use the concept of percent composition. The given nickel ore sample is 43.55% nickel by mass.
Let's assume the mass of the ore needed is 'x' grams. So, the mass of nickel in the ore becomes 0.4355x grams. Since 500.0 g of nickel is needed, we can set up the equation 0.4355x = 500.0 and solve for 'x' to find the amount of ore needed.
To solve the equation, we can divide both sides by 0.4355: x = 500.0 / 0.4355.
Using a calculator, we find that x is approximately 1147.29 grams. Therefore, approximately 1147.29 grams of ore are needed to obtain 500.0 g of nickel.