Answer:
- Density Liquid = 0.841 g/mL
- Density Metal = 2.711 g/cm³
Explanation:
- The density of the liquid is:
Mass Liquid / Volume Liquid
From the problem we know that Volume Liquid = 25.0 mL, <u>the mass of the liquid can be calculated by substracting masses</u>:
- Mass Liquid + Mass Slug + Mass Empty Cylinder = 125.934 g
- Mass Liquid + 15.454 g + 89.450 g = 125.934 g
- Mass Liquid = 125.934 g - 15.454 g - 89.450 g
Thus the density of the liquid is:
Density Liquid = 21.030 g / 25.0 mL = 0.841 g/mL
2. The density of the metal slug is:
Mass Metal / Volume Metal
We already know that the mass of the slug is 15.454 g. Its volume can be calculated using <em>Archimede's principle</em>, which states that the volume of an object is equal to the volume of liquid it displaces, in other words:
Volume Metal = 30.7 mL - 25.0 mL = 5.7 mL
Thus the density of the metal slug is
Density Metal = 15.454 g / 5.7 mL = 2.711 g/mL = 2.711 g/cm³
Answer:
<h2>14.05 moles</h2>
Explanation:
To find the number of moles in a substance given it's number of entities we use the formula
![n = \frac{N}{L} \\](https://tex.z-dn.net/?f=n%20%3D%20%20%5Cfrac%7BN%7D%7BL%7D%20%5C%5C)
where n is the number of moles
N is the number of entities
L is the Avogadro's constant which is
6.02 × 10²³ entities
From the question we have
![n = \frac{8.46 \times {10}^{24} }{6.02 \times {10}^{23} } \\ = 14.053156](https://tex.z-dn.net/?f=n%20%3D%20%20%5Cfrac%7B8.46%20%5Ctimes%20%20%7B10%7D%5E%7B24%7D%20%7D%7B6.02%20%5Ctimes%20%20%7B10%7D%5E%7B23%7D%20%7D%20%20%5C%5C%20%20%3D%2014.053156)
We have the final answer as
<h3>14.05 moles</h3>
Hope this helps you
Answer:
![\boxed {\boxed {\sf 7.89*10^{-4} \ mol \ Pb}}](https://tex.z-dn.net/?f=%5Cboxed%20%7B%5Cboxed%20%7B%5Csf%207.89%2A10%5E%7B-4%7D%20%5C%20mol%20%5C%20Pb%7D%7D)
Explanation:
To convert from moles to atoms, we must use Avogadro's Number. <u>Avogadro's Number</u>
- 6.022*10²³
- The number of particles (atoms, molcules, ions, etc.) in 1 mole.
- In this case, it is the number of atoms of lead.
1. Set up ratio
We can use Avogadro's Number as a fraction or ratio.
![\frac{6.022*10^{23} \ atoms \ Pb}{1 \ mol \ Pb}](https://tex.z-dn.net/?f=%5Cfrac%7B6.022%2A10%5E%7B23%7D%20%5C%20atoms%20%5C%20Pb%7D%7B1%20%5C%20mol%20%5C%20Pb%7D)
2. Convert atoms to moles
Multiply the given number of atoms by the ratio.
![4.75 *10^{20} \ atoms \ Pb *\frac{6.022*10^{23} \ atoms \ Pb}{1 \ mol \ Pb}](https://tex.z-dn.net/?f=4.75%20%2A10%5E%7B20%7D%20%5C%20atoms%20%5C%20Pb%20%2A%5Cfrac%7B6.022%2A10%5E%7B23%7D%20%5C%20atoms%20%5C%20Pb%7D%7B1%20%5C%20mol%20%5C%20Pb%7D)
Flip the fraction so that the atoms of lead can cancel each other out.
![4.75 *10^{20} \ atoms \ Pb *\frac{1 \ mol \ Pb}{6.022*10^{23} \ atoms \ Pb}](https://tex.z-dn.net/?f=4.75%20%2A10%5E%7B20%7D%20%5C%20atoms%20%5C%20Pb%20%2A%5Cfrac%7B1%20%5C%20mol%20%5C%20Pb%7D%7B6.022%2A10%5E%7B23%7D%20%5C%20atoms%20%5C%20Pb%7D)
![4.75 *10^{20} *\frac{1 \ mol \ Pb}{6.022*10^{23} }](https://tex.z-dn.net/?f=4.75%20%2A10%5E%7B20%7D%20%20%2A%5Cfrac%7B1%20%5C%20mol%20%5C%20Pb%7D%7B6.022%2A10%5E%7B23%7D%20%7D)
![\frac{4.75 *10^{20} \ mol \ Pb}{6.022*10^{23} }](https://tex.z-dn.net/?f=%5Cfrac%7B4.75%20%2A10%5E%7B20%7D%20%20%5C%20mol%20%5C%20Pb%7D%7B6.022%2A10%5E%7B23%7D%20%7D)
![7.88774494*10^{-4} \ mol \ Pb](https://tex.z-dn.net/?f=7.88774494%2A10%5E%7B-4%7D%20%5C%20mol%20%5C%20Pb)
3. Round
The original measurement of 4.75 had 3 significant figures (4, 7, and 5).
We must round our answer to 3 sig figs, which is the hundredth place for the number found.
![7.88774494*10^{-4} \ mol \ Pb](https://tex.z-dn.net/?f=7.88774494%2A10%5E%7B-4%7D%20%5C%20mol%20%5C%20Pb)
The 7 in the thousandth place tells us to round the 8 up to a 9 in the hundredth place.
![7.89*10^{-4} \ mol \ Pb](https://tex.z-dn.net/?f=7.89%2A10%5E%7B-4%7D%20%5C%20mol%20%5C%20Pb)
There are <u>7.89*10⁻⁴ moles of lead</u> in 4.75*10²⁰ atoms of lead.