Let's break down how to find the chemical formula for R-134a. R-134a is a common type of refrigerant, which are substances used in refrigeration and air conditioning systems.

Refrigerants are often named using an 'R-' number system. For many common refrigerants that are derived from alkanes (hydrocarbons with only single bonds), there's a specific way to figure out their chemical formula from the R-number.

Understanding the R-Numbering System for Refrigerants

The R-number for saturated (alkane-derived) refrigerants, like R-134a, can often be decoded using a simple rule:

R-abc, where:

• The first digit (a) is the number of Carbon atoms minus 1 (\(C - 1\)). If 'a' is 0, it's usually omitted.
• The second digit (b) is the number of Hydrogen atoms plus 1 (\(H + 1\)).
• The third digit (c) is the number of Fluorine atoms (\(F\)).
• The remaining valencies (bonds) on the carbon atoms are filled by Chlorine atoms (\(Cl\)).

Decoding the Formula for R-134a

For R-134a, the base number is 134. Let's apply the rules:

• Third digit is 4: This means there are 4 Fluorine (\(F\)) atoms. So, \(F = 4\).
• Second digit is 3: This means the number of Hydrogen atoms plus 1 is 3. So, \(H + 1 = 3\), which means \(H = 3 - 1 = 2\). There are 2 Hydrogen (\(H\)) atoms.
• First digit is 1: This means the number of Carbon atoms minus 1 is 1. So, \(C - 1 = 1\), which means \(C = 1 + 1 = 2\). There are 2 Carbon (\(C\)) atoms.

So far, we have a molecule with 2 Carbon atoms, 2 Hydrogen atoms, and 4 Fluorine atoms: \(C_2H_2F_4\).

Now let's check for Chlorine. Carbon atoms typically form 4 bonds. With 2 Carbon atoms, the total possible bonds are \(2 \times 4 = 8\). We assume a single bond between the two carbon atoms (\(C-C\)). This uses up 1 bond from each carbon, leaving 3 bonds on each carbon for other atoms, totaling 6 bonds available for Hydrogen and Fluorine (\(2 \times 3 = 6\)).

We have 2 Hydrogen and 4 Fluorine atoms, totaling \(2 + 4 = 6\) atoms attached to the carbons. These atoms use up 6 bonds. Since the number of available bonds (6) matches the number of bonds needed by Hydrogen and Fluorine (6), there are no Chlorine atoms (\(Cl = 0\)).

Thus, the chemical formula derived from the R-number 134 is \(C_2H_2F_4\).

The 'a' in R-134a indicates a specific isomer. R-134a corresponds to 1,1,1,2-tetrafluoroethane, which has the chemical formula \(C_2H_2F_4\). Other isomers of tetrafluoroethane (\(C_2H_2F_4\)), like 1,1,2,2-tetrafluoroethane, exist but might be designated differently (though 1,1,2,2-tetrafluoroethane is also sometimes referred to as R-134 or R-134(BLEND)). However, R-134a specifically refers to 1,1,1,2-tetrafluoroethane.

Analyzing the Options

Based on our derivation, the chemical formula is \(C_2H_2F_4\). Let's compare this to the given options:

• Option 1: \(C_2H_2F_3\) - Incorrect. It has only 3 Fluorine atoms.
• Option 2: \(C_2HF_4\) - Incorrect. It has only 1 Hydrogen atom.
• Option 3: \(C_2H_2F_4\) - Correct. This matches our derived formula.
• Option 4: \(C_3H_2F_4\) - Incorrect. It has 3 Carbon atoms instead of 2.

Therefore, the chemical formula of R-134a is \(C_2H_2F_4\).

Revision Table: Common Refrigerant Formulas

Additional Information on R-134a

R-134a (\(C_2H_2F_4\)) is a hydrofluorocarbon (HFC) refrigerant. It became widely used as a replacement for R-12 (\(CCl_2F_2\)) because R-12 is a chlorofluorocarbon (CFC) and was phased out due to its ozone-depleting potential.

Key characteristics and uses of R-134a:

• It has zero ozone depletion potential (ODP).
• It does have a global warming potential (GWP), although lower than many older refrigerants.
• Commonly used in automotive air conditioning, residential and commercial refrigeration, and chillers.
• It is non-flammable and non-toxic under normal conditions.

Understanding the chemical formula and properties of refrigerants like R-134a is important in the study of thermodynamics and refrigeration cycles.