Chapter 12, Problem 7STP

Interpretation Introduction

Interpretation :

Correct option must be chosen regarding the temperature and pressure at which solid graphite, solid diamond and liquid carbon coexists.

Concept Introduction :

Phase diagram gives the idea of different phases at different temperature and pressure. In the phase diagram of carbon, carbon can exit in solid diamond, solid graphite, liquid carbon and vapor phase. There are two triples points; in one point diamond, graphite and liquid carbon exist and in other point graphite liquid and vapor exist.

Answer to Problem 7STP

Correct answer: From the triple point, no option is correct as the point corresponds to ${10}^5\text{ atm }$ and approximately 3700 K.

Explanation of Solution

Reason for correct option: The given phase diagram of carbon is represented as follows:

  

The point marked is triple point where three phases that is diamond, liquid and graphite exist. From the graph it can be seen that this point is at ${10}^5\text{ atm }$ and approximately 3400 ^oC or approximately 3700 K.

Thus, none of the option is correct.

Conclusion

Reasons for incorrect options:

In option (a), the pressure and temperature is ${10}^6\text{ atm}$ and 4700 K respectively. Since, diamond cannot exist after approximately 3700 K and graphite cannot exist if pressure increases from ${10}^5\text{ atm}$ thus, option (a) is incorrect.

In option (b), the pressure and temperature is ${10}^3\text{ atm}$ and 3000 K respectively. Since, liquid carbon cannot exist if temperature is less than approximately 3700 K and diamond cannot exist if pressure decreases from ${10}^5\text{ atm}$ thus, option (b) is incorrect.

In option (c), the pressure and temperature is ${10}^5\text{ atm}$ and 5100 K respectively. The pressure value is correct but temperature cannot be greater than 3700 K. Thus, option (c) is incorrect.

In option (d), the pressure and temperature is 80 atm and 3500 K respectively. This cannot be possible as at this low pressure diamond will not exist.