\"Mathematics is a language in which one cannot express unprecise or nebulous th

Question

"Mathematics is a language in which one cannot express unprecise or nebulous thoughts." - Henri Poincaire The pressure and temperature at the surface of the planet Mars are p = 600. Nt/m^2, T = 218. K. Based on this information, find the number density (N/V, in units of molecules/cm^3) of molecules in the Martian atmosphere at surface level. Consider 1.0000 mol of oxygen gas (O_2) at a temperature T = 300.0 K and confined in a volume V = 4.0000 L. Find the pressure of the gas using: a) the ideal gas law b) the van der Waals equation (for O_2, a = 1.364 L^2 middot atm/mol^2, b = 3.19 times 10^2 L/mol) Give your calculated values for pressure to 4 significant figures. Which of the above values would you expect to be closer to the true value for pressure for the conditions in the problem? There are two naturally occurring isotopes of chlorine, ^35Cl(34.9688 amu) and^37Cl(36.9651 amu). While modern measurements of the percentage of each isotope of chlorine in nature are based on mass spectrometry, an approximate value for this percentage can be found from measurements on gases containing chlorine. The density of hydrogen chloride gas (HCl), measured at T = 18.3 degree C and p = 774.5 torr, is p = 1.554 g/L. Based on this information, and assuming that HCl obeys the ideal gas law, find the percentage of the^35Cl isotope in the sample of HCl. Note that naturally occurring hydrogen can be assumed to be all the^1H isotope (1.0078 amu). Compare your result to the value determined using mass spectrometry, percent^35Cl = 75.5 %. The one dimensional Maxwell-Boltzmann distribution of speeds of gas molecules is given by the expression f(v_x)dV_x = (M/2 pi RT)^1/2 exp(-Mv^2_x/2RT)dv_x; - infinity

Explanation / Answer

Q1.

P = 600 N/m2 = 600 Pa

T = 218 K

number density = N/V where N = units of molecule and V = cm3

This is, as marked in pencil, Ideal Gas Law, since it is pretty low Pressure and relatively speaking, high Temperature

so, use:

PV = nRT

solve for

n/V = P/(RT)

n/V = (600)/(8.314*218)

n/V = 0.33104 mol/m3

we need molecules per cm3

so

change mol

1 mol = 6.022*10^23 molecules

0.33104 mol --> 0.33104*6.022*10^23 = 1.99352*10^23 molecules per m3

1 m3 = 1000000 cm3

N/V = (1.99352*10^23 molecules / m3) * ( 1m3 / 1000000 cm3)

N/V =1.99352*10^17 molecules / cm3

density number = 1.99352*10^17 molecules / cm3

For all furhter questions, please pst them in multiple set of Q&A.

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