How much energy (in kilojoules) is required to convert 280mL of diethyl ether at its boiling point from liquid to vapor if its density is 0.7138 g/mL?
Its heat of vaporization is +26.5 kJ/mol at its boiling point.
Use the density to convert mL ether to grams.
Then q = mass x heat vaporization. You will need to change grams ether to moles or change heat vap to kJ/g. Watch the units.
To calculate the energy required to convert 280 mL of diethyl ether from liquid to vapor, we need to follow these steps:
Step 1: Convert the volume of diethyl ether to grams.
First, we need to determine the mass of diethyl ether using its density. The given density is 0.7138 g/mL.
Mass = Density × Volume
Mass = 0.7138 g/mL × 280 mL
Step 2: Calculate the moles of diethyl ether.
To calculate the moles, we need to divide the mass of diethyl ether by its molar mass. The molar mass of diethyl ether (C4H10O) is 74.12 g/mol.
Moles = Mass / Molar mass
Moles = (0.7138 g/mL × 280 mL) / 74.12 g/mol
Step 3: Calculate the energy required.
Using the heat of vaporization, we can calculate the energy required to convert the moles of diethyl ether from liquid to vapor. The given heat of vaporization is +26.5 kJ/mol.
Energy required = Moles of diethyl ether × Heat of vaporization
Energy required = (0.7138 g/mL × 280 mL) / 74.12 g/mol × 26.5 kJ/mol
Now, let's calculate the energy required step-by-step:
Mass = 0.7138 g/mL × 280 mL = 199.944 g
Moles = 199.944 g / 74.12 g/mol ≈ 2.697 mol
Energy required = 2.697 mol × 26.5 kJ/mol ≈ 71.368 kJ
Therefore, approximately 71.368 kilojoules (kJ) of energy is required to convert 280 mL of diethyl ether at its boiling point from liquid to vapor.
To determine the energy required to convert diethyl ether from liquid to vapor, we need to consider the following steps:
Step 1: Calculate the mass of diethyl ether.
The density of diethyl ether is given as 0.7138 g/mL. To find the mass, multiply the volume (in milliliters) by the density:
Mass = Volume x Density
Mass = 280 mL x 0.7138 g/mL
Step 2: Convert the mass of diethyl ether to moles.
To convert grams to moles, we need to divide the mass by the molar mass. The molar mass of diethyl ether is 74.12 g/mol. Therefore:
Moles = Mass / Molar Mass
Moles = (280 mL x 0.7138 g/mL) / 74.12 g/mol
Step 3: Calculate the energy required using the heat of vaporization.
The heat of vaporization is given as +26.5 kJ/mol. Multiply this value by the moles of diethyl ether determined in Step 2:
Energy = Heat of Vaporization x Moles
Energy = 26.5 kJ/mol x (280 mL x 0.7138 g/mL) / 74.12 g/mol
Now, plug in the values and calculate the energy required. Let's do the math:
Energy = 26.5 kJ/mol x (280 mL x 0.7138 g/mL) / 74.12 g/mol
Energy = 26.5 kJ x (0.280 L x 0.7138 g/mL) / 74.12 g
Energy = 5.740 kJ
Therefore, approximately 5.740 kilojoules of energy is required to convert 280 mL of diethyl ether from liquid to vapor at its boiling point.