What is the composition, in atom percent, of an alloy that contains \(44.5 \mathrm{lb}_{\mathrm{m}}\) of \(\mathrm{Ag}, 83.7 \mathrm{lb}_{\mathrm{m}}\) of Au, and \(5.3 \mathrm{lb}_{\mathrm{m}}\) of \(\mathrm{Cu}\) ?

To find the number of moles of each element, we can use the formula: n = m/M where 'n' is the number of moles, 'm' is the mass, and 'M' is the molar mass of the element. Molar masses (in g/mol): Ag = 107.87, Au = 196.97, Cu = 63.55 First, we need to convert the masses from lb_m to grams: 1 lb_m = 453.592 g Mass of Ag = 44.5 lb_m * 453.592 g/lb_m = 20159.644 g Mass of Au = 83.7 lb_m * 453.592 g/lb_m = 37967.3664 g Mass of Cu = 5.3 lb_m * 453.592 g/lb_m = 2404.0386 g Now, we will calculate the number of moles for each element by dividing the mass by its molar mass. moles of Ag = 20159.644 g / 107.87 g/mol = 186.8239 mol moles of Au = 37967.3664 g / 196.97 g/mol = 192.6984 mol moles of Cu = 2404.0386 g / 63.55 g/mol = 37.8338 mol

To find the total moles of all elements, we have to add the moles of individual elements: Total moles = moles of Ag + moles of Au + moles of Cu Total moles = 186.8239 mol + 192.6984 mol + 37.8338 mol = 417.3561 mol

To calculate the atom percent for each element, we can use the following formula: atom percent of an element = (number of moles of the element / total moles of all elements) * 100 Atom percent of Ag = (186.8239 mol / 417.3561 mol) * 100 = 44.76% Atom percent of Au = (192.6984 mol / 417.3561 mol) * 100 = 46.16% Atom percent of Cu = (37.8338 mol / 417.3561 mol) * 100 = 9.07% Therefore, the composition of the alloy is: 44.76% Ag, 46.16% Au, and 9.07% Cu.