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Chapter 11: Problem 81

A sample of gas at \(25.0^{\circ} \mathrm{C}\) and \(655 \mathrm{~mm} \mathrm{Hg}\) has a density of \(2.26 \times 10^{-3} \mathrm{~g} / \mathrm{mL}\). What is the molar mass of the compound?

Short Answer

Expert verified
The molar mass of the compound is approximately 53.4 g/mol, found using the ideal gas equation and given values, including a density of 2.26 × 10⁻³ g/mL, a pressure of 0.8618 atm, and a temperature of 298.15 K.

Step by step solution

01

Convert temperature to Kelvin and pressure to atm

Convert the temperature from Celsius to Kelvin using the following formula: T (K) = T (°C) + 273.15 T = 25 + 273.15 = 298.15 K Convert the pressure from mmHg to atm using the following conversion factor: 1 atm = 760 mmHg P = 655 mmHg × (1 atm / 760 mmHg) ≈ 0.8618 atm
02

Use the density and ideal gas equation to determine the mass and volume relationship

The density is given as: density = mass / volume = 2.26 × 10⁻³ g/mL Substituting the ideal gas equation into the density equation, we get: density = (n × molar mass) / (n × RT / P)
03

Solve for the molar mass

Rearrange the equation from Step 2 to isolate the molar mass: molar mass = (density × P × RT) / n Since we want to find the molar mass of the compound, we don't need to find the number of moles (n). We can rewrite the equation as follows: molar mass = density × P × RT Now, substitute the known values and constants: molar mass = (2.26 × 10⁻³ g/mL) × (0.8618 atm) × (0.0821 L·atm/mol·K) × (298.15 K) Note: The ideal gas constant, R, is equal to 0.0821 L·atm/mol·K. molar mass ≈ 53.4 g/mol The molar mass of the compound is approximately 53.4 g/mol.

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Most popular questions from this chapter

Perform the following conversions: (a) \(30.2\) in. \(\mathrm{Hg}\) to millimeters of mercury (b) \(890.0 \mathrm{~mm} \mathrm{Hg}\) to atmospheres (c) \(300.0 \mathrm{lb} / \mathrm{in} .^{2}\) to atmospheres

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