Question

Following the dimensional analysis below, what would the resulting units be? \[ (90 \mathrm{mEq} / 4 \text { hours })(1 \mathrm{~L} / 100 \mathrm{mEq})(1 \mathrm{hour} / 60 \text { minutes })(1,000 \m

Answer 1

The resulting units after the dimensional analysis are
`\(1.5 \, \mathrm{L/min}\)`.

Step-by-step explanation:

In dimensional analysis, we use the given values to cancel out units and find the desired result. Let's break down the calculation step by step:

`1. \(90 \, \mathrm{mEq}/4 \, \mathrm{hours}\)`: This expression involves the ratio of milliequivalents to time. To eliminate the unit of hours, we multiply by
`\(1 \, \mathrm{hour}/60 \, \mathrm{minutes}\)` resulting in
`\(\frac{90 \, \mathrm{mEq}}{240 \, \mathrm{minutes}}\)`.

2.
`\(\frac{90 \, \mathrm{mEq}}{240 \, \mathrm{minutes}} * \frac{1 \, \mathrm{L}}{100 \, \mathrm{mEq}}\)`: This part introduces the conversion factor from milliequivalents to liters. By multiplying with
`\(1 \, \mathrm{L}/100 \, \mathrm{mEq}\)`, the milliequivalent unit cancels out, leaving us with
`\(\frac{0.9 \, \mathrm{L}}{240 \, \mathrm{minutes}}\)`.

3.
`\(\frac{0.9 \, \mathrm{L}}{240 \, \mathrm{minutes}} * \frac{60 \, \mathrm{minutes}}{1 \, \mathrm{hour}}\): This step converts minutes to hours by multiplying with \(60 \, \mathrm{minutes}/1 \, \mathrm{hour}\), resulting in \(\frac{0.9 \, \mathrm{L}}{4 \, \mathrm{hours}}\)`.

4. The final expression is
`\(\frac{0.9 \, \mathrm{L}}{4 \, \mathrm{hours}} * \frac{1,000 \, \mathrm{mL}}{1 \, \mathrm{L}}\), which simplifies to \(1.5 \, \mathrm{L/min}\)`.

In summary, by carefully applying conversion factors to cancel out units, we arrive at the final answer of
`\(1.5 \, \mathrm{L/min}\)`, representing the rate of the given quantity.