The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53 . The unknown vapor had a mass of $2.55 \mathrm{~g} ;\( the volume of the bulb was \)500 \mathrm{~mL}\(, pressure \)101.33 \mathrm{kPa}\(, and temperature \)37^{\circ} \mathrm{C.Calculate}$ the molar mass of the unknown vapor.

Short Answer

Expert verified
The molar mass of the unknown vapor can be calculated using the ideal gas law and the given information. After converting the temperature to Kelvin and pressure to atm, we find the number of moles using the ideal gas law and then calculate the molar mass by dividing the mass by the number of moles. The molar mass of the unknown vapor is approximately 130.1 g/mol.

Step by step solution

01

Convert temperature to Kelvin

The given temperature is in Celsius, so we need to convert it to Kelvin by adding 273.15 to the Celsius value. Hence, the temperature in Kelvin is \(T = 37 + 273.15 = 310.15 \mathrm{K}\).
02

Convert pressure to atm

The pressure is given in kPa, but the ideal gas constant R has the unit L atm mol^{-1} K^{-1}. To be consistent, we need to convert the pressure to atm using the conversion factor 1 atm = 101.325 kPa. Therefore, the pressure in atm is \(P = \frac{101.33 \mathrm{kPa}}{101.325\, \mathrm{kPa/atm}} = 1 \mathrm{atm}\).
03

Calculate the number of moles of the unknown vapor

Now we can use the ideal gas law to find the number of moles \(n\): \(PV = nRT \Rightarrow n = \frac{PV}{RT}\). Plugging in the given values, we have: \(n = \frac{(1\, \mathrm{atm})(0.5\, \mathrm{L})}{(0.0821\, \mathrm{L\, atm\, mol^{-1}K^{-1}})(310.15\, \mathrm{K})} = 0.0196\, \mathrm{mol}\)
04

Calculate the molar mass of the unknown vapor

We have the mass of the unknown vapor and the number of moles calculated in the previous step. We can now find the molar mass (M) by dividing the mass by the number of moles: \(M = \frac{\mathrm{mass}}{\mathrm{moles}} = \frac{2.55 \mathrm{g}}{0.0196\, \mathrm{mol}} = 130.1\, \mathrm{g/mol}\) The molar mass of the unknown vapor is approximately 130.1 g/mol.

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Most popular questions from this chapter

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