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Chapter 10: Problem 54

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 0.846 g; the volume of the bulb was \(354 \mathrm{cm}^{3},\) pressure 752 torr, and temperature \(100^{\circ} \mathrm{C}\) . Calculate the molar mass of the unknown vapor.

Short Answer

Expert verified
The molar mass of the unknown vapor is approximately \(27.8 \: g/mol\).

Step by step solution

01

Convert given units to appropriate SI units

First, we need to convert all given values to appropriate SI units to use the ideal gas law equation. The pressure needs to be in pascals (Pa), volume needs to be in meters cubed (m³), and the temperature needs to be in kelvin (K). The given values are: - Pressure (P) = 752 torr - Volume (V) = 354 cm³ - Temperature (T) = 100°C - Mass (m) = 0.846 g Convert them to SI units: - P = 752 torr × (101325 Pa / 760 torr) ≈ 100662 Pa - V = 354 cm³ × (1 m³ / 1000000 cm³) = 3.54 × 10⁻⁴ m³ - T = 100°C + 273.15 = 373.15 K
02

Apply ideal gas law equation to find the number of moles

The ideal gas law equation is: PV = nRT We can solve for the number of moles (n) using the equation: n = PV / RT Substitute the converted values of P, V, and T, and use the R value for SI units (8.314 J/(mol·K)): n = (100662 Pa * 3.54 × 10⁻⁴ m³) / (8.314 J/(mol·K) * 373.15 K) ≈ 0.0304 moles
03

Calculate the molar mass

The molar mass (M) of the substance can be calculated by dividing the mass by the number of moles: M = mass (g) / n (moles) Substitute the values for mass and the number of moles we just calculated: M = 0.846 g / 0.0304 moles ≈ 27.8 g/mol The molar mass of the unknown vapor is approximately 27.8 g/mol.

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Most popular questions from this chapter

(a) If the pressure exerted by ozone, \(\mathrm{O}_{3},\) in the stratosphere is \(3.0 \times 10^{-3}\) atm and the temperature is 250 \(\mathrm{K}\) , how many ozone molecules are in a liter? (b) Carbon dioxide makes up approximately 0.04\(\%\) of Earth's atmosphere. If you collect a \(2.0-\mathrm{L}\) sample from the atmosphere at sea level \((1.00 \mathrm{atm})\) on a warm day \(\left(27^{\circ} \mathrm{C}\right),\) how many \(\mathrm{CO}_{2}\) molecules are in your sample?

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of \(\mathrm{Cl}_{2}\) gas is 8.70 \(\mathrm{L}\) at 895 torr and \(24^{\circ} \mathrm{C}\) .(a) How many grams of \(\mathrm{Cl}_{2}\) are in the sample? (b) What volume will the \(\mathrm{Cl}_{2}\) occupy at \(\mathrm{STP}\) ? (c) At what temperature will the volume be 15.00 \(\mathrm{L}\) if the pressure is \(8.76 \times 10^{2}\) torr? (d) At what pressure will the volume equal 5.00 L if the temperature is \(58^{\circ} \mathrm{C}\) ?

Perform the following conversions: \((\mathbf{a})\) 0.912 atm to torr, \((\mathbf{b})\) 0.685 bar to kilopascals, \((\mathbf{c})\) 655 \(\mathrm{mm}\) Hg to atmospheres, \((\mathbf{d})\) \(1.323 \times 10^{5}\) Pa to atmospheres, \((\mathbf{e})\) 2.50 atm to psi.

Indicate which of the following statements regarding the kinetic-molecular theory of gases are correct. (a) The average kinetic energy of a collection of gas molecules at a given temperature is proportional to \(m^{1 / 2}\) . (b) The gas molecules are assumed to exert no forces on each other. (c) All the molecules of a gas at a given temperature have the same kinetic energy. (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained. (e) All gas molecules move with the same speed if they are at the same temperature.

(a) Calculate the number of molecules in a deep breath of air whose volume is 2.25 L at body temperature, \(37^{\circ} \mathrm{C},\) and a pressure of 735 torr. (b) The adult blue whale has a lung capacity of \(5.0 \times 10^{3} \mathrm{L}\) . Calculate the mass of air (assume an average molar mass of 28.98 \(\mathrm{g} / \mathrm{mol}\) ) contained in an adult blue whale's lungs at \(0.0^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm},\) assuming the air behaves ideally.
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