Answer
$4.03125 \times 10^{27}$ molecules
Work Step by Step
We have a room that is 5m by 10m by 3m.
Each cubic meter contains 1000L of gas.
And every 22.4L of gas contains $6.02 \times 10^{23}$ molecules. We need to calculate how many molecules are in this room.
So first we calculate how many cubic feet this room is. which is Length x Width x Height.
$5\times10\times3 = 150$ cubic meters.
Next let's calculate how many liters there are in this room.
$150 \times 1000 = 150000$
Now we need to divide 150000L by 22.4.
$150000 \div 22.4 = 6696.429$
And finally we need to multiply 6696.429 by $6.02 \times 10^{23}$. To simplify this process, let's first convert 6696.429 into scientific notation and then multiply.
$6696.429 = 6.696429 \times 10^3$
$(6.696429 \times 10^3) (6.02 \times 10^{23})$
$6.02 * 6.696429 = 40.3125$ and $10^{3+23} = 10^{26}$
So we have an answer of $40.3125 \times 10^{26}$ but that's not in proper scientific notation. We need to move the decimal point over to the left one space and that will add +1 to the exponent on the power of 10. giving us our final answer of:
$4.03125 \times 10^{27}$
