A sample of 5.00 mL of diethylether 1C2H5OC2H5,density = 0.7134 g>mL2 is introduced into a 6.00-L vesselthat already contains a mixture of N2 and O2, whose partialpressures are PN2 = 21.08 kPa and PO2 = 76.1 kPa. The temperatureis held at 35.0 °C, and the diethylether totally evaporates.(b) Calculate the total pressure in the container.

Verified step by step guidance

1. Calculate the mass of diethyl ether using its volume and density: \( \text{mass} = \text{volume} \times \text{density} \).
2. Convert the mass of diethyl ether to moles using its molar mass: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
3. Use the ideal gas law to find the partial pressure of diethyl ether: \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
4. Add the partial pressures of N2, O2, and diethyl ether to find the total pressure in the container: \( P_{\text{total}} = P_{\text{N2}} + P_{\text{O2}} + P_{\text{diethyl ether}} \).
5. Ensure all pressures are in the same units (e.g., kPa) before adding them to find the total pressure.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under varying conditions and is crucial for calculating the total pressure in a container when new gases are introduced.

Partial Pressure

Partial pressure is the pressure exerted by an individual gas in a mixture of gases. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of each component. This concept is vital for determining the contribution of diethylether to the overall pressure in the vessel after it evaporates.

Density and Molar Mass

Density is defined as mass per unit volume and is crucial for converting the volume of a liquid into mass. Molar mass, the mass of one mole of a substance, allows for the calculation of the number of moles present. In this problem, the density of diethylether is used to find its mass, which is then converted to moles to apply the Ideal Gas Law.