Problem

A cube of gold that is 1.00 cm on a side has a mass of 19.3 g. A single gold atom has a mass of 197.0 u. (b) From the information given, estimate the diameter in Å of a single gold atom.

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Hi everyone here we have a question asking us to calculate the diameter in angstrom of a silver atom. A silver moller mass, 107.87 a. M. You cube with an edge of one centimeter has a mass of 10.49 g. So first we want to calculate the mass of a single silver atom. So we're going to use our 0.87 grams of silver and that's its molar mass, which is in grams per mole. So that's per one mole of silver. We're going to multiply it by one mole of silver Over avocados number which is 6.02, 2 Times 10 to the 23rd silver atoms. So our moles here are going to cancel out And that is going to give us 1. one, three times 10 To the negative grams per adam. Next we want to assume that there's a one centimeter by one centimeter by one centimeter cube. So we're going to use 0.49 grams of silver over one cube Times one Silver Atom over The number. We just calculated 1.791, 3 Times 10 to the negative grams and our grams of silver are canceling out here. So we get five .856, 1 Times 10 to the silver Adams per cube. Now we're going to assume that the cube has no empty space so the volume of a silver atom is going to equal one centimeter cubed over 5. Times 10 to the 22 silver atoms, which equals one .707, 6 Times 10 to the negative 23 centimeters per silver adam. Now that we know the volume of a silver atom, we're going to use the formula volume equals four thirds pie times radius cubed and we want radius isolated. So the radius is going to equal 3/4 volume divided by pi To the 1 3rd power and plugging in what we know, We get three fours Times 1.707, 6 Times 10 to the negative centimeters cubed divided by pi To the 1 3rd power And that equals 1.597. 4 Times 10 to the negative eight cm. So that is our radius and all of our diameter is is our radius times two. So we're going to do two times point 597, 4 Times 10 to the negative eight cm. And we're going to change that to angstrom. So times 10 to the eight angstrom over one centimeter. And our centimeters are canceling out and that equals 3.19 Angstrom. And that is our final answer. Thank you for watching. Bye