Even though the numbers are in scientific notation, they are still just numbers. Essentially the question is as simple as "An apple weighs an ounce, how much do 35 apples weigh?". So all you have to do is multiply.
3.25 x
![10^{-22}](https://tex.z-dn.net/?f=%2010%5E%7B-22%7D%20)
x 6.0 x
![10^{23}](https://tex.z-dn.net/?f=%2010%5E%7B23%7D%20)
= 195
Answer:
The ideal molar volume is
The Z factor is ![Z = 0.09997](https://tex.z-dn.net/?f=Z%20%3D%200.09997)
The real molar volume is ![\frac{V_r}{n} = V_k= 0.0001095\ \frac{m^3}{mol}](https://tex.z-dn.net/?f=%5Cfrac%7BV_r%7D%7Bn%7D%20%3D%20V_k%3D%20%20%200.0001095%5C%20%5Cfrac%7Bm%5E3%7D%7Bmol%7D)
Explanation:
From the question we are told that
The pressure is
The temperature is ![T = 30 ^ oC = 303 \ K](https://tex.z-dn.net/?f=T%20%20%3D%20%2030%20%5E%20oC%20%20%3D%20303%20%5C%20K)
According to the ideal gas equation we have that
![PV = nRT](https://tex.z-dn.net/?f=PV%20%20%3D%20%20nRT)
=> ![\frac{V}{n}=V_z= \frac{RT}{P}](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Bn%7D%3DV_z%3D%20%5Cfrac%7BRT%7D%7BP%7D)
Where
is the molar volume and R is the gas constant with value
![R = 8.314 \ m^3 \cdot Pa \cdot K^{-1}\cdot mol^{-1}](https://tex.z-dn.net/?f=R%20%20%3D%20%208.314%20%5C%20m%5E3%20%5Ccdot%20Pa%20%5Ccdot%20K%5E%7B-1%7D%5Ccdot%20mol%5E%7B-1%7D)
substituting values
![\frac{V}{n} =V_z= \frac{ 8.314 * 303}{23 *10^{5}}](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Bn%7D%20%20%3DV_z%3D%20%20%5Cfrac%7B%208.314%20%2A%20%20303%7D%7B23%20%2A10%5E%7B5%7D%7D)
The compressibility factor of the gas is mathematically represented as
![Z = \frac{P * V_z}{RT}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BP%20%2A%20%20V_z%7D%7BRT%7D)
substituting values
![Z = \frac{23 *10^{5} * 0.001095}{8.314 * 303}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B23%20%2A10%5E%7B5%7D%20%2A%20%20%200.001095%7D%7B8.314%20%2A%20303%7D)
![Z = 0.09997](https://tex.z-dn.net/?f=Z%20%3D%200.09997)
Now the real molar volume is evaluated as
![\frac{V_r}{n} = V_k= \frac{Z * RT }{P}](https://tex.z-dn.net/?f=%5Cfrac%7BV_r%7D%7Bn%7D%20%3D%20V_k%3D%20%20%5Cfrac%7BZ%20%2A%20%20RT%20%7D%7BP%7D)
substituting values
![\frac{V_r}{n} = V_k= \frac{0.09997 * 8.314 * 303}{23 *10^{5}}](https://tex.z-dn.net/?f=%5Cfrac%7BV_r%7D%7Bn%7D%20%3D%20V_k%3D%20%20%20%5Cfrac%7B0.09997%20%2A%20%208.314%20%2A%20%20303%7D%7B23%20%2A10%5E%7B5%7D%7D)
![\frac{V_r}{n} = V_k= 0.0001095\ \frac{m^3}{mol}](https://tex.z-dn.net/?f=%5Cfrac%7BV_r%7D%7Bn%7D%20%3D%20V_k%3D%20%20%200.0001095%5C%20%5Cfrac%7Bm%5E3%7D%7Bmol%7D)
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If you drop a bath bomb into water, then it will fizz because a chemical reaction is taking place.