What pressure in mmHg is equivalent to 1.350 atm
The Correct Answer and Explanation is:
The correct answer is 1026 mmHg.
Explanation
This problem requires the conversion of a pressure value from one unit, atmospheres (atm), to another unit, millimeters of mercury (mmHg). This is a common calculation in chemistry and physics, and it relies on a standard, defined relationship between these two units of pressure.
The fundamental conversion factor that connects atmospheres and millimeters of mercury is:
1 atm = 760 mmHg
This equality states that one standard atmosphere of pressure is equivalent to the pressure exerted by a column of mercury that is 760 millimeters high. This relationship is an exact definition, meaning it does not have any uncertainty and will not limit the significant figures in a calculation.
To solve the problem, we use a method called dimensional analysis. This involves setting up the calculation so that the original units cancel out, leaving only the desired units. We start with the given value, 1.350 atm, and multiply it by the conversion factor arranged as a fraction. To cancel the ‘atm’ unit, it must be in the denominator of the fraction.
The setup for the conversion is as follows:
Pressure in mmHg = 1.350 atm × (760 mmHg / 1 atm)
By performing this multiplication, the ‘atm’ unit in the numerator of the starting value cancels with the ‘atm’ unit in the denominator of the conversion factor, leaving mmHg as the final unit.
The calculation is:
1.350 × 760 = 1026
An important final step is to consider the significant figures. The initial measurement, 1.350 atm, has four significant figures (the trailing zero after the decimal point is significant). Because the conversion factor of 760 mmHg per 1 atm is an exact number, the precision of our answer is determined solely by the starting value. Therefore, our final answer must also have four significant figures. The calculated result, 1026, already has exactly four significant figures, so no rounding is necessary.
