First, we need to determine the value of the constant K using the given data. We can use any of the given data points to solve for K. Let's use the first data point:y = 0.15 fractional surface coverage x = 0.01 atm pressure 0.15 = K * 0.01 / 1 + K * 0.01 Now, we need to solve for K:0.15 + 0.15 * K * 0.01 = K * 0.010.15 = K * 0.01 - 0.15 * K * 0.01^20.15 = K * 0.01 1 - 0.15 * 0.01 K = 0.15 / 0.01 * 1 - 0.0015 K 15.79Now that we have the value of K, we can use the Langmuir isotherm equation to find the fractional surface coverage y at a pressure of 0.1 atm:x = 0.1 atmy = 15.79 * 0.1 / 1 + 15.79 * 0.1 y 0.941The fractional surface coverage at 0.1 atm is approximately 0.941, which means that 94.1% of the surface is covered by the adsorbed gas. Since we are assuming a monolayer coverage, the surface area of the metal oxide sample can be calculated by dividing the total surface area by the fractional surface coverage:Total surface area = Surface area of the metal oxide sample / Fractional surface coverageSurface area of the metal oxide sample = Total surface area * Fractional surface coverageHowever, we do not have enough information to determine the total surface area or the surface area of the metal oxide sample. We would need additional information, such as the amount of gas adsorbed or the size of the adsorbed molecules, to calculate the surface area.