Final answer:
To find the mass of gold(III) chloride containing a trillion chlorine atoms, the number of moles of chlorine atoms is first computed, then converted to moles of gold(III) chloride. The molar mass of gold(III) chloride is used to finally calculate the mass, which is 0.00017 g when rounded to two significant figures.
Step-by-step explanation:
To answer the question, we need to calculate the mass of gold(III) chloride (AuCl3) that contains a trillion chlorine atoms. Gold(III) chloride has the formula AuCl3, meaning we have 3 moles of chlorine for every mole of gold(III) chloride. We will find the molar mass of AuCl3 and then use it to calculate the corresponding mass that contains a trillion chlorine atoms.
Step 1: Calculate the number of moles of chlorine atoms in a trillion (1.0 x 1012) chlorine atoms using Avogadro's number (6.022 x 1023 atoms/mol).
1.0 x 1012 atoms Cl × × (1 mol Cl / 6.022 x 1023 atoms Cl) = 1.661 x 10-12 moles Cl.
Step 2: Calculate the moles of gold(III) chloride (AuCl3) needed by dividing the moles of chlorine by 3.
1.661 x 10-12 moles Cl ÷ (3 Cl atoms/mol AuCl3) = 5.537 x 10-13 moles AuCl3.
Step 3: Determine the molar mass of AuCl3 using average atomic masses: Au (approximately 197.0 g/mol) and Cl (35.45 g/mol).
197.0 g/mol (Au) + 3 × 35.45 g/mol (Cl) = 303.35 g/mol (AuCl3).
Step 4: Calculate the mass of AuCl3 that corresponds to the moles determined in Step 2.
5.537 x 10-13 moles AuCl3 × 303.35 g/mol = 0.0001678 g of AuCl3, which rounds to 0.00017 g when using two significant figures.