Question

22) A gaseous element has a density of 6.607 g/L when the temperature is 36.01 degrees C and the pressure is 744.8 torr. What is the molecular mass (g/mol) of the gas? Keep the answer with 2 decimal places

Answer 1

Step 1

Gases are assumed to be ideal. Therefore, it is used:

p x V = n x R x T

p = pressure = 744.8 torr (1 atm = 760 torr) => 744.8 torr x (1 atm/760 torr) = 0.98 atm

T = absolute temperature = 36.01 °C + 273 = 309.01 K

V = volume

R = gas constant = 0.082 atm x L/mol x K

n = number of moles = mass/molar mass = m/M

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Step 2

p x V = n x R x T can be written as:

`\begin{gathered} p\text{ x V = }(m)/(M)\text{ x R x T} \\ p\text{ = }(m)/(VxM)xRxT \\ p\text{ = }(m)/(V)x\text{ }(RxT)/(M) \\ Clear\text{ M and m/V = density:} \\ M=density\text{ x }(RxT)/(p) \\ M\text{ = 6.607 g/L x }\frac{0.082\text{ atm x L/mol x K x 309.01K}}{0.98\text{ atm}} \\ \end{gathered}`

Answer: Molar mass = 170.83 g/mol