Question

ethanol is a chemical that is used in many hand sanitizers. it is produced when steam reacts with the chemical ethylene. consider the following reaction: 4 molecules of ethylene (c₂h₄) react with 4 molecules of water (h₂o) to produce some amount of ethanol (c₂h₆o). complete the table below. during this reaction, how many molecules of ethanol (c₂h₆o) are produced?

Explanation:

Step1: Calculate the number of \(H\) atoms

• In \(C_{2}H_{4}\): Each \(C_{2}H_{4}\) has \(4\) \(H\) atoms. \(4\) molecules of \(C_{2}H_{4}\) have \(4\times4 = 16\) \(H\) atoms.
• In \(H_{2}O\): Each \(H_{2}O\) has \(2\) \(H\) atoms. \(4\) molecules of \(H_{2}O\) have \(4\times2=8\) \(H\) atoms.
• Total \(H\) atoms: \(16 + 8=24\) (before reaction). After reaction, in \(C_{2}H_{6}O\), let the number of \(C_{2}H_{6}O\) molecules be \(x\). Each \(C_{2}H_{6}O\) has \(6\) \(H\) atoms. By conservation of atoms, \(6x=24\) (but wait, original calculation: \(4\) \(C_{2}H_{4}\) (\(4\times4 = 16\) \(H\)) and \(4\) \(H_{2}O\) (\(4\times2 = 8\) \(H\)): total \(H=16 + 8=24\). Wait no, correct: \(4\) \(C_{2}H_{4}\): \(4\times4=16\) \(H\); \(4\) \(H_{2}O\): \(4\times 2 = 8\) \(H\). Total \(H=16+8 = 24\). But wait, formula of ethanol \(C_{2}H_{6}O\). Let \(n\) be the number of ethanol molecules. \(H\) atoms: \(6n\). Also, from reactants: \(4\) \(C_{2}H_{4}\) (\(H:4\times4 = 16\)) and \(4\) \(H_{2}O\) (\(H:4\times2=8\)). Total \(H = 16 + 8=24\). \(6n=24\) (no, wait, wrong approach. Count atoms directly. \(4\) \(C_{2}H_{4}\): \(4\times4 = 16\) \(H\); \(4\) \(H_{2}O\): \(4\times2=8\) \(H\). Total \(H=16 + 8=24\). But in ethanol \(C_{2}H_{6}O\), if \(4\) molecules (as we'll find), \(4\times6=24\) \(H\)

Step2: Calculate the number of \(C\) atoms

• In \(C_{2}H_{4}\): Each \(C_{2}H_{4}\) has \(2\) \(C\) atoms. \(4\) molecules of \(C_{2}H_{4}\) have \(4\times2 = 8\) \(C\) atoms. There is no \(C\) in \(H_{2}O\). So total \(C\) atoms \(=8\)

Step3: Calculate the number of \(O\) atoms

• In \(H_{2}O\): Each \(H_{2}O\) has \(1\) \(O\) atom. \(4\) molecules of \(H_{2}O\) have \(4\times1=4\) \(O\) atoms. There is no \(O\) in \(C_{2}H_{4}\). So total \(O\) atoms \(=4\)

Step4: Find the number of ethanol molecules

• For \(C\): Let the number of \(C_{2}H_{6}O\) molecules be \(x\). Each \(C_{2}H_{6}O\) has \(2\) \(C\) atoms. From reactants, \(C\) atoms from \(C_{2}H_{4}\): \(4\times2=8\). So \(2x = 8\), \(x = 4\). Check for \(O\): Each \(C_{2}H_{6}O\) has \(1\) \(O\) atom. \(x = 4\) gives \(4\) \(O\) atoms (matches from \(H_{2}O\): \(4\) molecules of \(H_{2}O\) give \(4\) \(O\) atoms). For \(H\): Each \(C_{2}H_{6}O\) has \(6\) \(H\) atoms. \(4\) molecules give \(4\times6 = 24\) \(H\) atoms (\(4\) \(C_{2}H_{4}\) give \(4\times4=16\) \(H\) and \(4\) \(H_{2}O\) give \(4\times2 = 8\) \(H\), total \(16+8=24\))

Answer:

• For \(H\): \(28\)
• For \(C\): \(8\)
• For \(O\): \(4\)
• Molecules of ethanol: \(4\)