Problem 100 - Chemistry Matter and Change

Question

a. Write the balanced equation for the synthesis of ethanol from ethene and water. b. If 448 L of ethene gas reacts with excess water at STP, how many grams of ethanol will be produced? (Chapter 13)

Step-by-Step Solution

Answer

The balanced chemical equation for the synthesis of ethanol from ethene and water is: \(C_2H_4 + H_2O → C_2H_5OH\). When 448 L of ethene gas reacts with excess water at STP, 921.4 grams of ethanol will be produced.

Step 1: Write the balanced chemical equation for the synthesis of ethanol

To write a balanced chemical equation, we need to make sure that the number of atoms for each element on the reactants side equals the number of atoms for each element on the products side. For the synthesis of ethanol from ethene and water, we have: Ethene + Water → Ethanol C2H4 + H2O → C2H5OH Both sides of the equation are balanced, with 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom.

Step 2: Determine the moles of ethene gas at STP

At STP, the gas occupies 22.4 L per mole. We can use this to determine the moles of ethene gas in 448 L: Moles of ethene = (volume of ethene at STP) / (22.4 L/mol) Moles of ethene = 448 L / 22.4 L/mol Moles of ethene = 20 mol

Step 3: Use stoichiometry to determine the moles of ethanol produced

Now, we can use stoichiometry to determine the moles of ethanol produced from 448 L of ethene gas, according to the balanced chemical equation. Since 1 mol of ethene reacts with 1 mol of water to produce 1 mol of ethanol: Moles of ethanol = moles of ethene = 20 mol

Step 4: Calculate the mass of ethanol produced

Finally, we can calculate the mass of the ethanol produced using the molar mass of ethanol. The molar mass of ethanol is: C2H5OH = 2(12.01 g/mol) + 6(1.01 g/mol) + 1(16.00 g/mol) = 46.07 g/mol Now we can calculate the mass of ethanol produced: Mass of ethanol = moles of ethanol × molar mass of ethanol Mass of ethanol = 20 mol × 46.07 g/mol Mass of ethanol = 921.4 g So, 921.4 grams of ethanol will be produced when 448 L of ethene gas reacts with excess water at STP.

Key Concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It's like a recipe for chemical reactions, where you need the right proportions to get the desired product.

• First, you must understand the balanced equation of a reaction as it serves as the base for any stoichiometric calculations.
• In stoichiometry, you need to know how to convert units such as liters to moles (or vice versa) using conditions such as STP (Standard Temperature and Pressure).
• The ratio from the balanced equation helps us predict how much product we can get from a given amount of reactant.

In our example, from the balanced equation, we see that each mole of ethene gas reacts with one mole of water to produce one mole of ethanol. Thus, knowing the moles of ethene gives us the moles of ethanol.

Balanced Chemical Equations

A balanced chemical equation accurately represents the chemical reaction by having an equal number of atoms for each element on both sides of the equation.To balance an equation:

• Write down the unbalanced equation.
• Count the atoms of reactants and products for each element.
• Add coefficients in front of compounds to ensure an equal number of atoms on both sides.

In the synthesis of ethanol, the equation is originally written as:\[ \text{C}_2\text{H}_4 + \text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_5\text{OH} \]

• This equation is balanced as it has 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom on both sides.
• Balancing ensures no atoms are lost or gained, which aligns with the law of conservation of mass.

Molar Mass Calculations

Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is crucial for converting moles to grams and vice versa.

• To find the molar mass of a compound, sum the atomic masses of its constituent elements.
• For example, ethanol \[ \text{C}_2\text{H}_5\text{OH} \] has a molar mass calculated as: \[ 2(12.01) + 6(1.01) + 16.00 = 46.07 \text{ g/mol} \]
• Once the molar mass is known, use it to convert moles of a substance to grams, as shown in the ethanol synthesis where 20 moles were converted to 921.4 grams.

Synthesis of Ethanol

The synthesis of ethanol involves the chemical reaction between ethene and water, producing ethanol as the result. This process is predominantly used in industries to produce ethanol on a large scale.

• The reaction is represented by the equation: \[ \text{C}_2\text{H}_4 + \text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_5\text{OH} \]
• This is a type of addition reaction, where water is added across the double bond of ethene to form ethanol.
• Industrially, this is usually done under controlled conditions to optimize yield and efficiency.

Understanding how this synthesis works, helps us visualize and calculate potential yields, as seen when converting ethene's volume at STP to ethanol's mass.