A balloon is filled with helium gas to a gauge pressure of 22 mm Hg at 25^∘ C. The volume of the

step 1 In this question, we have a balloon that is filled with helium gas to a gorge pressure of 22mm m

A balloon is filled with helium gas to a gauge pressure of...

A balloon is filled with helium gas to a gauge pressure of $22 \mathrm{mm}$ Hg at $25^{\circ} \mathrm{C}$. The volume of the gas is $305 \mathrm{mL},$ and the barometric pressure is $755 \mathrm{mm}$ Hg. What amount of helium is in the balloon? (Remember that gauge pressure = total pressure - barometric pressure. See page $452 .$ )

A balloon is filled with helium gas to a gauge pressure of $22 \mathrm{mm}$ Hg at $25^{\circ} \mathrm{C}$. The volume of the gas is $305 \mathrm{mL},$ and the barometric pressure is
$755 \mathrm{mm}$ Hg. What amount of helium is in the balloon? (Remember that gauge pressure = total pressure - barometric pressure. See page $452 .$ )

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Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is used to relate a gas's pressure (P), volume (V), number of moles (n), and temperature (T) through the gas constant (R). It is fundamental in calculating the quantity of gas present when the state variables are known.

Gauge and Absolute Pressure

Gauge pressure measures the pressure relative to the atmospheric pressure. To obtain the absolute pressure of a gas, which is required in thermodynamic calculations like the Ideal Gas Law, the ambient (barometric) pressure is added to the gauge pressure.

Units Conversion

Accurate application of physical laws such as the Ideal Gas Law requires converting all quantities into consistent units. This includes converting temperatures to Kelvin, pressures to an absolute scale (if given in mm Hg or other units), and ensuring the volume is in proper units.

Fundamental Gas Constants

Using fundamental constants like the ideal gas constant (R) is crucial when applying the Ideal Gas Law. Consistent usage of these constants along with conversion factors ensures that the calculated number of moles is accurate.

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