An 11.5-mL sample of liquid butane (density = 0.573 g/mL) is evaporated in an otherwise empty container at a temperature of 28.5 °C. The pressure in the container following evaporation is 892 torr. What is the volume of the container?

Verified step by step guidance

1. Convert the pressure from torr to atm using the conversion factor: 1 atm = 760 torr.
2. Calculate the mass of butane using the formula: mass = volume \times density.
3. Convert the mass of butane to moles using the molar mass of butane (C_4H_{10}).
4. Use the ideal gas law equation, PV = nRT, to solve for the volume of the container (V).
5. Ensure that the temperature is converted to Kelvin by adding 273.15 to the Celsius temperature before using it in the ideal gas law equation.

Key Concepts

Density and Mass Calculation

Density is defined as mass per unit volume, typically expressed in grams per milliliter (g/mL). To find the mass of the liquid butane, you can use the formula: mass = density × volume. In this case, with a density of 0.573 g/mL and a volume of 11.5 mL, the mass can be calculated, which is essential for further calculations involving the gas phase.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. Here, P is pressure in atmospheres, V is volume in liters, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law is crucial for determining the volume of the container after the butane has evaporated.

Conversion of Units

In chemistry, it is often necessary to convert units to ensure consistency in calculations. For example, pressure may need to be converted from torr to atmospheres, and volume from milliliters to liters. Understanding how to perform these conversions is vital for accurately applying the Ideal Gas Law and obtaining the correct volume of the container.