Main answer: The pressure of the 0.200 mol-sample of He gas is 5.70 atm.
Explanation: We can use the ideal gas law formula to calculate the pressure of the given gas sample. The formula is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. We can rearrange this formula to solve for pressure, which gives us P = nRT/V.
Substituting the given values into the formula, we get P = (0.200 mol) x (0.08206 L atm/mol K) x (345 K) / 4.15 L = 5.70 atm.
Therefore, the pressure of the 0.200 mol-sample of He gas is 5.70 atm.
Conclusion: The pressure of a gas sample can be calculated using the ideal gas law formula, which involves the variables of pressure, volume, number of moles, gas constant, and temperature. By substituting the given values into the formula and solving for pressure, we can determine the pressure of the gas sample, which in this case is 5.70 atm.