The value for the gas constant R is 1.987 cal/mol·K or 62.37 L·mmHg/mol·K or 0.08314 L·bar/mol·K. The equality 1 atm = 76 cm Hg is an exact equality. Using this given information, determine how many atm corresponds to exactly 1 bar.
The Correct Answer and Explanation is :
To determine how many atmospheres (atm) correspond to exactly 1 bar, we will first need to utilize the given relationships between units of pressure. Let’s break it down step by step:
- Given Data:
- 1 atm = 76 cm Hg (an exact equality).
- 1 bar = 100,000 pascals (Pa) (known fact).
- 1 atm = 101,325 Pa (known fact).
- We are also given that 1 atm = 76 cm Hg, and this is key to establishing the relationship between atm and bar.
- Convert 1 Bar to Atmospheres:
First, let’s express 1 bar in terms of cm Hg, since we know the relationship between atm and cm Hg.
- From the known relation: 1 atm = 76 cm Hg.
- 1 bar = 100,000 Pa, and we know that 1 atm is also equal to 101,325 Pa. To convert bar to atm, we first convert bar to pascals, then pascals to atm using the conversion factor. [
\frac{1 \, \text{atm}}{101,325 \, \text{Pa}} = \frac{x \, \text{atm}}{100,000 \, \text{Pa}}
] Now, solve for (x), the number of atmospheres in 1 bar: [
x = \frac{100,000 \, \text{Pa}}{101,325 \, \text{Pa}} \, \text{atm}
] [
x = 0.9869 \, \text{atm}
] Thus, 1 bar is equivalent to approximately 0.9869 atm.
- Conclusion:
The value for 1 bar is nearly equal to 1 atm but slightly less. Specifically, 1 bar is about 0.9869 atm. This conversion shows how the two units of pressure relate based on the known physical constants for the atmospheric pressure and the bar measurement.