A sample of an ideal gas has a volume of 0.00100 m3, a pressure of 4.50 atmospheres and 2.00 × 1023 particles. What is the temperature of the gas?

To solve this problem, we can use the ideal gas law equation, which is PV = nRT.

1. First, we need to convert the pressure from atmospheres to Pascals because the gas constant (R) we are going to use is in Pascals. 1 atmosphere is approximately equal to 101325 Pascals. So, 4.50 atmospheres is equal to 4.50 * 101325 = 456,462.5 Pascals.

2. Next, we need to calculate the number of moles (n). We know that 1 mole of any substance contains approximately 6.022 x 10^23 particles (Avogadro's number). So, 2.00 x 10^23 particles is equal to 2.00 x 10^23 / 6.022 x 10^23 = 0.332 moles.

3. Now we can substitute the values into the ideal gas law equation. The gas constant (R) is 8.3145 J/(mol.K). So, the equation becomes 456,462.5 Pascals * 0.00100 m^3 = 0.332 moles * 8.3145 J/(mol.K) * T.

4. Solving for T (temperature), we get T = (456,462.5 Pascals * 0.00100 m^3) / (0.332 moles * 8.3145 J/(mol.K)) = 137,800 Kelvin.

So, the temperature of the gas is approximately 137,800 Kelvin.