Final answer:
The number of vacancies per cubic meter can be calculated using the ideal gas law and Avogadro's number. At standard temperature and pressure, the number of vacancies per cubic meter is 44.5.
Step-by-step explanation:
The number of vacancies per cubic meter can be calculated using the ideal gas law.
At standard temperature and pressure (STP), which is defined to be 0°C and atmospheric pressure, the number of molecules per cubic meter of gas is 2.68×10^25.
To find the number of vacancies per cubic meter, we divide the number of molecules by Avogadro's number. The formula for the number of vacancies per cubic meter is:
n = N/Na
where n is the number of vacancies per cubic meter, N is the number of molecules per cubic meter, and Na is Avogadro's number.
Therefore, the number of vacancies per cubic meter at 1000 is:
n = (2.68×10^25) / (6.022×10^23) = 44.5 vacancies/m³