The value of gas constant R (in cal/mol-K) for hydrogen is:

• A) ½
• B) 2
• C) 4
• D) 1

The gas constant R is a fundamental constant in thermodynamics and plays a crucial role in various equations, including the ideal gas law. When considering the value of R specifically for hydrogen in calories per mole per Kelvin (cal/mol-K), we need to look at the standard value of R and how it relates to different units.

Understanding the Gas Constant R

The universal gas constant R is commonly expressed in several units. The most frequently used values are:

• 8.314 J/(mol·K) in joules
• 0.0821 L·atm/(mol·K) in liters and atmospheres
• 1.987 cal/(mol·K) in calories

Conversion to Calories

When we convert the value of R from joules to calories, we use the conversion factor that 1 calorie is approximately 4.184 joules. Therefore, to convert R from joules to calories, we can use the following calculation:

R = 8.314 J/(mol·K) ÷ 4.184 J/cal = 1.987 cal/(mol·K)

Identifying the Value for Hydrogen

In the context of your question, the value of R does not change based on the gas being considered; it remains a universal constant. Thus, for hydrogen, the value of R in cal/mol-K is still 1.987 cal/(mol·K). When looking at the options provided:

• A) ½
• B) 2
• C) 4
• D) 1

The closest answer to the actual value of R (1.987) is option B) 2.

Conclusion

To summarize, the value of the gas constant R for hydrogen, expressed in calories per mole per Kelvin, is approximately 1.987 cal/(mol·K). Therefore, the correct answer from the options given is B) 2. This value is essential for calculations involving gas behavior under various conditions, making it a key concept in thermodynamics and physical chemistry.