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## Q. 8.8

Using Avogadro’s Law: Finding moles in a Given Volume at STP
Use the standard molar volume of a gas at STP (22.4 L) to find how many moles of air at STP are in a room measuring 4.11 m wide by 5.36 m long by 2.58 m high.
ANALYSIS We first find the volume of the room and then use standard molar volume as a conversion factor to find the number of moles.

## Verified Solution

STEP 1: Identify known information.          Length = 5.36 m
We are given the room dimensions.             Width = 4.11 m                                                                                                           Height = 2.58 m

STEP 2: Identify answer and units.                    Moles of air = ?? mol

STEP 3: Identify the equation. The
volume of the room is the product of
its three dimensions. Once we have the
volume (in m³), we can convert to liters
and use the molar volume at STP as a
conversion factor to obtain moles of air.

Volume = (4.11 m)(5.36m)(2.58 m) = 56.8 m³

= 56.8 m³×$\frac {1000L}{1m³} = 5.68 ×10^{4} L$

1mol= 22.4 L→ $\frac {1 mol}{22.4L}$

STEP 4: Solve. Use the room volume and
the molar volume at STP to set up an equation, making sure unwanted units cancel.

$5.68 × 10^{4} \cancel{L} × \frac {1 mol}{ 22.4 \cancel { L}} = 2.54 × 10^{3} mol$