How many atoms are in a 2.0 cm×2.0 cm×2.0 cm cube of aluminum?

Video transcript

Hey everyone. So this problem is asking us to calculate the number of atoms in a three centimeter by four centimeter by five centimeter right rectangular prism of copper. Our multiple choice answers here are a 5.87 times 10 to the 24 atoms. B 5.07 times 10 to the 24 atoms. C 6.15 times 10 to the 22 atoms or D 6.67 times 10 to the 22 atoms. So the key to solving this problem is recalling that the number of atoms N is given by the equation M lowercase M which is our mass divided by upper case M which is our molar mass. So the mass of this prism of copper is going to be given by the equation M equals row V where row is our density and V is our volume. In turn, our volume of this rectangular prism is given by our length multiplied by our width multiplied by our height. And so the density of copper is a constant. We can recall or look up that it is 8920 kg per meters cubed and then our length. Now, our length, width and height were all given in centimeters. But we need to keep these in standard units of meters. So we'll rewrite that as 0.03 m, a length of 0.04 m and a height of 0.05 m. We multiply that all together and we're left with a mass of 0. kg. Now we have to find our molar mass or uppercase M and again, for copper are atomic weight is 63.546 U. And we can recall that you is a constant 1.66 times 10 to the negative 27 kg. And so when we plug that in, we get a molar mass of 1.055 times 10 to the negative 25 kg. And now all we have to do is plug that back into our first equation. Those two values we just found 0. kg divided by 1.0 55 times 10 to the negative 25 kg. And we're left with 5.07 times 10 to the 24 atoms. And so that is the correct answer for this problem and it aligns with answer choice B. So that's all we have for this one. We'll see you in the next video.