Question: will the melting and freezing point of any pure substance be the same

Answer: No, For most substances, melting and freezing points are approximately equal. For example, the melting point and freezing point of mercury is 234.32 kelvins (−38.83 °C or −37.89 °F). However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts at 85 °C (185 °F) and solidifies from 31 °C (88 °F; 304 K); such direction dependence is known as hysteresis. The melting point of ice at 1 atmosphere of pressure is very close to 0 °C (32 °F; 273 K); this is also known as the ice point. In the presence of nucleating substances, the freezing point of water is not always the same as the melting point. In the absence of nucleators water can exist as a supercooled liquid down to −48.3 °C (−55°F, 224.8 K) before freezing. The chemical element with the highest melting point is tungsten, at 3,414 °C (6,177 °F; 3,687 K); this property makes tungsten excellent for use as filaments in light bulbs. The often-cited carbon does not melt at ambient pressure but sublimes at about 3,726.85 °C (6,740.33 °F; 4,000.00 K); a liquid phase only exists above pressures of 10 MPa (99 atm) and estimated 4,030--4,430 °C (7,290--8,010 °F; 4,300--4,700 K) (see carbon phase diagram). Tantalum hafnium carbide (TaHfC) is a refractory compound with a very high melting point of 4215 K (3942 °C, 7128 °F). At the other end of the scale, helium does not freeze at all at normal pressure even at temperatures close to absolute zero; pressure greater than twenty times of atmosphere of normal one is necessary.