Which of these statements describes this mathematical equation? (P_(1)V_(1))/(T_(1))=k The final pressure of a gas is directly proportional to volume and temperature change. The final pressure of a gas is inversely proportional to the volume change and directly proportional to temperature change. The final pressure of a gas is directly proportional to volume change and inversely proportional to temperature change. none of the above

The given equation \(\frac{P_{1}V_{1}}{T_{1}}=k\) is a form of the ideal gas law, where \(P_1\), \(V_1\), and \(T_1\) are the initial pressure, volume, and temperature of a gas, respectively, and \(k\) is a constant. This equation implies that for a given amount of gas, the ratio of the product of pressure and volume to the temperature remains constant.<br /><br />To analyze the statements:<br /><br />1. "The final pressure of a gas is directly proportional to volume and temperature change." - This statement is incorrect because it suggests direct proportionality to both volume and temperature, which does not align with the equation.<br /><br />2. "The final pressure of a gas is inversely proportional to the volume change and directly proportional to temperature change." - This statement is also incorrect because it misrepresents the relationships described by the equation.<br /><br />3. "The final pressure of a gas is directly proportional to volume change and inversely proportional to temperature change." - This statement is incorrect as well because it does not accurately describe the relationship in the equation.<br /><br />4. "None of the above." - This is the correct choice since none of the provided statements accurately describe the relationship expressed by the equation \(\frac{P_{1}V_{1}}{T_{1}}=k\).<br /><br />Therefore, the correct answer is: **none of the above**.