Which depth of mercury column produces a pressure of 1.00 atm at standard gravity?

• A. 760 mm
• B. 1.00 m
• C. 273 mm
• D. 101.3 mm

Answer: (A)

Verified step by step guidance

1. Understand that the pressure exerted by a column of liquid is given by the hydrostatic pressure formula: \(P = \rho g h\), where \(P\) is the pressure, \(\rho\) is the density of the liquid, \(g\) is the acceleration due to gravity, and \(h\) is the height (or depth) of the liquid column.
2. Identify the known values: the pressure \(P\) is 1.00 atm, which can be converted to pascals (Pa) using the conversion \$1\ \text{atm} = 101325\ \text{Pa}\(; the density \)\rho\( of mercury is approximately \)13,600\ \text{kg/m}^3\(; and the standard acceleration due to gravity \)g\( is \)9.80665\ \text{m/s}^2$.
3. Rearrange the hydrostatic pressure formula to solve for the height \(h\) of the mercury column: \(h = \frac{P}{\rho g}\).
4. Substitute the known values into the rearranged formula: \(h = \frac{101325\ \text{Pa}}{13600\ \text{kg/m}^3 \times 9.80665\ \text{m/s}^2}\).
5. Calculate \(h\) to find the height in meters, then convert this height to millimeters by multiplying by 1000, since 1 meter = 1000 millimeters. This will give the depth of the mercury column that produces a pressure of 1.00 atm.