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What is the molar mass of an unknown gas with a density of 2.65 g/L at 3.00 atm and 45.0 °C?

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In order to solve this question, we will need to use two very common formulas, the first it will be the Ideal gas Law, but with a few changes, and the second it will be the density formula:

PV = nRT, this is the Ideal gas formula, and we have:

P = 3.00 atm

T = 45°C, but we need it in Kelvin, 318 K

R = 0.082, this is the gas constant

d = m/V, this is the density formula, and we have:

d = 2.65 g/L

Now let's make a few changes on the ideal gas formula, first switching n (number of moles) for m/MM (mass/molar mass)

PV = m/MM * RT

P*MM/RT = m/V, now we have m/V, which is the same as density, now we can use the values

3 * MM/0.082 * 318 = 2.65

3 * MM/26.076 = 2.65

3MM = 69.10

MM = 23.03g/mol, this is the final molar mass

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