Rewrite the ideal gas law solving for \(T\). Also show how all units cancel to leave you with just units of temperature.

Write down the ideal gas law equation: PV = nRT

To solve for T, we need to isolate T on one side of the equation. Divide both sides by nR: \(T = \frac{PV}{nR}\) Now T is isolated and the equation is rewritten solving for temperature T.

To show how all units cancel to leave us with just units of temperature, let's break down the units for each variable: - P (pressure) has units of Pascals (Pa) or N/m² (Newtons per square meter) - V (volume) has units of cubic meters (m³) - n (number of moles) has units of moles (mol) - R (ideal gas constant) has units of J/(mol K) (Joules per mol per Kelvin) Now let's substitute these units into the equation we found in Step 2: \(\frac{N/m² * m³}{mol * J/(mol*K)}\) We can see that several units cancel out: - moles (mol) in both the numerator and denominator - meters (m) in both the numerator and denominator: m² in the denominator and m³ in the numerator, leaving m¹ (meters) in the numerator This leaves us with the following units: \(\frac{N * m}{J / K}\) We can further simplify the units by recognizing that the Newton-meter (Nm) is equivalent to Joules (J): \(\frac{J}{J / K} \) Finally, we see that the Joules (J) cancel out, leaving us with: K (Kelvin) This is the unit of temperature and confirms that our rewritten equation for T is correct: \(T = \frac{PV}{nR}\)