To find the number of moles of nitrogen gas (N2) present in a 1.75 L sample at standard temperature and pressure (STP), you can use the ideal gas law. However, at STP, we have a simpler way to calculate the number of moles because one mole of any ideal gas occupies 22.414 liters at STP.
Here are the step-by-step instructions to calculate the number of moles:
1. Note the volume of nitrogen gas given: [tex]\( V_{\text{gas}} = 1.75 \)[/tex] liters.
2. Recognize that at STP, one mole of an ideal gas occupies [tex]\( V_{\text{molar}} = 22.414 \)[/tex] liters.
3. Use the ratio of the volume of gas to the molar volume at STP to find the number of moles of nitrogen gas:
[tex]\[ \text{Number of moles of N}_2 = \frac{V_{\text{gas}}}{V_{\text{molar}}} \][/tex]
Now we can substitute the given values into the equation:
[tex]\[ \text{Number of moles of N}_2 = \frac{1.75}{22.414} \][/tex]
4. Simply divide the volume of the nitrogen gas by the molar volume at STP to find the number of moles:
[tex]\[ \text{Number of moles of N}_2 = 0.078059 \][/tex]
So, there are approximately 0.078059 moles of nitrogen gas in a 1.75 L sample at STP.
