Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant b. If the temperature of a gas increases from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C},\) the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

According to Avogadro's law, equal volumes of gases at the same temperature and pressure have the same number of moles. So, if we double the number of moles of a gas while keeping pressure and temperature constant, the volume will also double. Thus, statement a is true.

For this statement, we will use Charles's law, which states that for a given amount of gas at constant pressure, the volume of the gas is directly proportional to its temperature. It is important to use the Kelvin scale for temperature. Convert the temperatures to Kelvin: \(25^{\circ} \mathrm{C} = 298 \mathrm{K}\) \(50^{\circ} \mathrm{C} = 323 \mathrm{K}\) To see if the volume doubles when the temperature increases from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\), calculate the ratio of the temperatures: \( \frac{323 \mathrm{K}}{298 \mathrm{K}} \approx 1.084 \) Since the ratio is not equal to 2, the volume does not double when the temperature increases from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) with constant pressure and number of moles. So, statement b is false.

A barometer is a scientific instrument used to measure atmospheric pressure. So, statement c is true.

For this statement, we will use Boyle's law, which states that for a given amount of gas at constant temperature, the volume of the gas is inversely proportional to its pressure. Let the initial volume and pressure be V1 and P1, and the final volume and pressure be V2 and P2. As the volume decreases by half, we have: \( V2 = \frac{1}{2} V1 \) By Boyle's law, \( P1 \times V1 = P2 \times V2 \), which implies: \( P1 \times V1 = P2 \times \frac{1}{2}V1 \) Divide both sides by V1: \( P1 = \frac{1}{2} P2 \) The pressure would have to double for this equality to hold: \( P2 = 2P1 \) Thus, statement d is true. The correct answers are statements a, c, and d.