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What volume of aluminum has the same number of atoms as 10 cm3 of mercury?

Short Answer

Expert verified

The Volume of aluminum is 6.8cm3

Step by step solution

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01

Description 

In terms of calculating the macroscopic system state variables are going to be used.

The ฯis one of the densities of state variables and is defined through the ratio of another two-state variable and it is provided through the equation (18.1) in the form

ฯ=MVV=Mฯ (1)

Then, the atoms' number N is provided through equation (18.4) in the form

N=MmM=mN

In this case, N is the atoms' number and m is molecular mass. The M's expression is going to be used in equation (1)

V=mNp(2)N=pVm(3)

The mercury's molecular mass is mHg=200u and density is pHg=13600kg/m3.

The equation (3) is going to be used in order to get NHgthrough:

localid="1651396197699" N=pVm=(13600kg/m3)(10ร—10-6m3)200ร—1.66ร—10-27kg=4.09ร—1023atoms

02

Result 

The aluminium has the same numbers as the subject of atoms. Therefore equation (2) is going to be used to get the volume.

Aluminium's molecular mass is mAI=27u

density is pAI=2700kg/m3

V=mNp{"x":[[4,9,20,21,32,37],[56,83],[57,83],[102,185,267],[143,142,143,143,149,159,163,162,163,163,168,178,185,183],[193,193,193,223,223,221],[169,167,174,184,197,199,194,183,168]],"y":[[47,95,155,155,96,48],[112,112],[134,133],[132,132,132],[50,115,115,59,50,50,64,114,114,64,50,49,58,115],[115,8,9,115,116,8],[266,153,148,148,158,189,204,210,210]],"t":[[0,0,0,0,0,0],[0,0],[0,0],[0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0]],"version":"2.0.0"}

localid="1651396213148" =(27ร—1.66ร—10-27kg)(4.09ร—1023atoms)2700kg/m3=6.8ร—10-6m3=6.8c.m3

Therefore, the result is6.8cm3

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