%3Cp%3E%3Cspan%20class%3D%22c1%22%3EA%2020.0%3C%2Fspan%3E%3Cspan%20class%3D%0A%2

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%3Cp%3E%3Cspan%20class%3D%22c1%22%3EA%2020.0%3C%2Fspan%3E%3Cspan%20class%3D%0A%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_25_1397004055015_12%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-1-Frame%22%3E%3Cspan%20class%3D%22c5%22%3E%3Cspan%20class%3D%0A%22c4%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-2%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-3%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-4%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-5%22%3Ec%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-6%22%3Em%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%0A%3Cspan%20class%3D%22c1%22%3E-diameter%20cylinder%20of%20helium%20gas%20is%0A50.0%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_25_1397004055015_22%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-2-Frame%22%3E%3Cspan%20class%3D%22c5%22%3E%3Cspan%20class%3D%0A%22c4%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-8%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-9%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-10%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-11%22%3Ec%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-12%22%3Em%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%20long%0Aand%20at%2030.0%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_25_1397004055015_25%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-3-Frame%22%3E%3Cspan%20class%3D%22c13%22%3E%3Cspan%20class%3D%0A%22c12%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-14%22%3E%3Cspan%20class%3D%0A%22msubsup%20c3%22%20id%3D%22MathJax-Span-15%22%3E%3Cspan%20class%3D%22c11%22%3E%3Cspan%20class%3D%0A%22c8%22%3E%3Cspan%20class%3D%22mi%20c3%22%20id%3D%0A%22MathJax-Span-16%22%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c10%22%3E%3Cspan%20class%3D%0A%22mo%20c9%22%20id%3D%0A%22MathJax-Span-17%22%3E%3F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3EC.%0AThe%20pressure%20gauge%20reads%20130%3C%2Fspan%3E%3Cspan%20class%3D%0A%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_25_1397004055015_28%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-4-Frame%22%3E%3Cspan%20class%3D%22c15%22%3E%3Cspan%20class%3D%0A%22c14%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-19%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-20%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-21%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-22%22%3Ep%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-23%22%3Es%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-24%22%3Ei%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3B.%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3E%3Cbr%20%2F%3E%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EA.%3C%2Fspan%3E%3Cspan%20class%3D%22c16%22%3EHow%20many%20helium%0Aatoms%20are%20in%20the%20cylinder%3F%20atoms%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c16%22%3EB.%3C%2Fspan%3E%3Cspan%20class%3D%22c16%22%3EWhat%20is%20the%20mass%20of%0Athe%20helium%3F%20kg%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c17%22%3EC.%3C%2Fspan%3E%3Cspan%20class%3D%22c16%22%3EWhat%20is%20the%20helium%0Anumber%20density%3F%20attoms%2Fm%5E3%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c16%22%3ED.%3C%2Fspan%3E%3Cspan%20class%3D%22c16%22%3EWhat%20is%20the%20helium%0Amass%20density%3F%20kg%2Fm%5E3%3C%2Fspan%3E%3C%2Fp%3E%0A

Explanation / Answer

(1) Volume of a cylinder is given by

V = ?*(r^2)*h

Now calculate the volume of the cylinder.

V = ?*(r^2)*h
V = (3.1416)*((0.20 m/2)^2)*(0.50 m)
V = 0.0157 m^3

(2) Calculate the number of moles of helium present in the cylinder

PV = nRT
n = PV/RT
n = ((130 psi)*(1 atm/14.7 psi)*(0.0157 m^3)) / ((0.08206 L?atm?K^?1?mol^?1)*(30 + 273.15))
n = 0.138 / 24.91
n = 5.57*10^-3 moles

The other calculations should be straightforward from there:


How many helium atoms are in the cylinder?

Number of helium atoms
= (5.57*10^-3 moles)*(6.02 x 10^23 atoms/mole)
(6.02 x 10^23 mol^-1) is Avogadro's number)

= 3.35*10^21 atoms of helium


What is the mass of the helium?

Mass of the helium
= ( (5.57*10^-3 moles)*(4.002 g/mol)
= 0.022229 g
= 0.000022 Kg (2.229*10^-5 kg)


What is the helium number density?

Helium number density
= (number of atoms)/(volume of cylinder)
= 3.35*10^21 / 0.0157
= 2.135*10^23 atoms/m^3


What is the helium mass density

Helium mass density
= (mass of the helium)/(volume of the cylinder)
= 0.000022 / 0.0157
= 1.415*10^-3 kg/m^3
= 0.001415 kg/m^3

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